{"id":36546,"date":"2025-08-27T06:59:03","date_gmt":"2025-08-27T06:59:03","guid":{"rendered":"https:\/\/mp.moonpreneur.com\/math-corner\/?p=36546"},"modified":"2025-08-28T08:50:18","modified_gmt":"2025-08-28T08:50:18","slug":"arithmetic-progression","status":"publish","type":"post","link":"https:\/\/mp.moonpreneur.com\/math-corner\/arithmetic-progression\/","title":{"rendered":"Arithmetic Progression (AP) \u2013 Definition, Formula, and Solved Examples"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"36546\" class=\"elementor elementor-36546\" data-elementor-post-type=\"post\">\n\t\t\t\t\t\t<div class=\"elementor-inner\">\n\t\t\t\t<div class=\"elementor-section-wrap\">\n\t\t\t\t\t\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-32db9e5 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"32db9e5\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-1c303cd\" data-id=\"1c303cd\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-ed01562 elementor-widget elementor-widget-text-editor\" data-id=\"ed01562\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<h3><b>Introduction<\/b><\/h3>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-c122d8a elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"c122d8a\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-558dcd4\" data-id=\"558dcd4\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-f1935a1 elementor-widget elementor-widget-text-editor\" data-id=\"f1935a1\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<p><span style=\"font-weight: 400;\">Arithmetic Progression (AP) is one of the most important concepts in mathematics. It represents a sequence of numbers where the difference between consecutive terms remains constant. This simple yet powerful idea is widely used in mathematics, physics, finance, and even in our daily lives.<\/span><\/p>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-c6ae772 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"c6ae772\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-78a477f\" data-id=\"78a477f\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-d2a429c elementor-widget elementor-widget-text-editor\" data-id=\"d2a429c\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<h3><b>Table of Contents<\/b><\/h3>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-27afaa6 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"27afaa6\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-bc80616\" data-id=\"bc80616\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-8c49706 elementor-widget elementor-widget-text-editor\" data-id=\"8c49706\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<ol>\n \t<li><span style=\"font-weight: 400;\"><a href=\"#1\"> What is Arithmetic Progression (AP)?<\/a><\/span><\/li>\n \t<li><span style=\"font-weight: 400;\"><a href=\"#2\">\u00a0Standard Notation in Arithmetic Progression<\/a><\/span><\/li>\n \t<li><span style=\"font-weight: 400;\"><a href=\"#3\">\u00a0General Form of AP<\/a><\/span><\/li>\n \t<li><span style=\"font-weight: 400;\">\u00a0<\/span><span style=\"font-weight: 400;\"><a href=\"#4\"> nth Term of AP Formula<\/a><\/span><\/li>\n \t<li><span style=\"font-weight: 400;\">\u00a0<\/span><span style=\"font-weight: 400;\"><a href=\"#5\">Sum of n Terms Formula<\/a><\/span><\/li>\n \t<li><span style=\"font-weight: 400;\">\u00a0<\/span><span style=\"font-weight: 400;\"><a href=\"#6\">Types of Arithmetic Progression<\/a><\/span><\/li>\n \t<li><span style=\"font-weight: 400;\">\u00a0<\/span><span style=\"font-weight: 400;\"><a href=\"#7\"> Examples and Solutions<\/a><\/span><\/li>\n \t<li><span style=\"font-weight: 400;\"> \u00a0<\/span><span style=\"font-weight: 400;\"><a href=\"#8\">Practice Problems<\/a><\/span><\/li>\n \t<li>\u00a0<a href=\"#9\">FAQs on Arithmetic Progression<\/a><\/li>\n<\/ol>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-2bf564b elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"2bf564b\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-298b6ee\" data-id=\"298b6ee\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-ccf46f6 elementor-widget elementor-widget-text-editor\" data-id=\"ccf46f6\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<h3><b><a id=\"1\"><\/a>What is Arithmetic Progression (AP)?<\/b><\/h3>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-17fc098 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"17fc098\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-be7a92e\" data-id=\"be7a92e\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-e6edeb5 elementor-widget elementor-widget-image\" data-id=\"e6edeb5\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-image\">\n\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"739\" height=\"492\" src=\"https:\/\/mp.moonpreneur.com\/math-corner\/wp-content\/uploads\/2025\/08\/nth-term-of-AP-formula.webp\" class=\"attachment-medium_large size-medium_large wp-image-36548\" alt=\"What is Arithmetic Progression (AP)?\" loading=\"lazy\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-e4b6e50 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"e4b6e50\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-c1e45d9\" data-id=\"c1e45d9\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-af69ce0 elementor-widget elementor-widget-text-editor\" data-id=\"af69ce0\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<p><span style=\"font-weight: 400;\">Arithmetic Progression (AP) is one of the most common types of mathematical sequences. It is defined as a <\/span><b>sequence of numbers in which the difference between two consecutive terms remains constant<\/b><span style=\"font-weight: 400;\">.<\/span><\/p><p><span style=\"font-weight: 400;\">\ud83d\udc49 Example:<\/span><\/p><ul><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">2, 4, 6, 8, 10 \u2026 (Common difference = 2)<\/span><span style=\"font-weight: 400;\"><br \/><\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">5, 10, 15, 20 \u2026 (Common difference = 5)<\/span><span style=\"font-weight: 400;\"><br \/><\/span><\/li><\/ul><p><span style=\"font-weight: 400;\">This fixed difference is called the <\/span><b>common difference (d)<\/b><span style=\"font-weight: 400;\">.<\/span><\/p><p><span style=\"font-weight: 400;\">We observe APs in real life too:<\/span><\/p><ul><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Seat numbers in classrooms<\/span><span style=\"font-weight: 400;\"><br \/><\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Dates in a calendar<\/span><span style=\"font-weight: 400;\"><br \/><\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Even &amp; odd numbers<\/span><span style=\"font-weight: 400;\"><br \/><\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Roll numbers in a list<\/span><\/li><\/ul>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-3ff4b35 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"3ff4b35\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-22e2d20\" data-id=\"22e2d20\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-5910a22 elementor-widget elementor-widget-text-editor\" data-id=\"5910a22\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<h3><b><a id=\"2\"><\/a>Standard Notation in Arithmetic Progression<\/b><\/h3>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-1a279b8 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"1a279b8\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-a2c24c1\" data-id=\"a2c24c1\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-284e2e4 elementor-widget elementor-widget-html\" data-id=\"284e2e4\" data-element_type=\"widget\" data-widget_type=\"html.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<p>In an AP, the following notations are commonly used:<\/p>\n\n<table border=\"1\" cellpadding=\"8\" cellspacing=\"0\">\n  <thead>\n    <tr>\n      <th>Term<\/th>\n      <th>Representation<\/th>\n      <th>Formula<\/th>\n    <\/tr>\n  <\/thead>\n  <tbody>\n    <tr>\n      <td>First Term<\/td>\n      <td>a<\/td>\n      <td>&mdash;<\/td>\n    <\/tr>\n    <tr>\n      <td>Common Difference<\/td>\n      <td>d<\/td>\n      <td>\\(a_{2} - a_{1}\\)<\/td>\n    <\/tr>\n    <tr>\n      <td>nth Term<\/td>\n      <td>\\(a_{n}\\)<\/td>\n      <td>\\(a + (n - 1) \\times d\\)<\/td>\n    <\/tr>\n    <tr>\n      <td>Sum of First n Terms<\/td>\n      <td>\\(S_{n}\\)<\/td>\n      <td>\\(\\frac{n}{2} \\big[2a + (n - 1)d\\big]\\)<\/td>\n    <\/tr>\n  <\/tbody>\n<\/table>\n<style>\ntable {\n  font-family: arial, sans-serif;\n  border-collapse: collapse;\n  width: 100%;\n  \n}\nth{background-color: #21618C;color:#fff;}\ntd, th {\n  border: 1px solid #000;\n  text-align: center;\n  padding: 8px;\n}\n \ntr:nth-child(odd) {  \n  background-color: #eeeeee;  \n}\n<\/style>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-17695ee elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"17695ee\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-8fad6b5\" data-id=\"8fad6b5\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-c596ce5 elementor-widget elementor-widget-text-editor\" data-id=\"c596ce5\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<h3><b><a id=\"3\"><\/a>General Form of AP<\/b><\/h3>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-94fefd8 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"94fefd8\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-1845075\" data-id=\"1845075\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-6893ce0 elementor-widget elementor-widget-text-editor\" data-id=\"6893ce0\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<p><span style=\"font-weight: 400;\">An AP can be written as:\u00a0 <\/span><strong>\\(a, \\; a + d, \\; a + 2d, \\; a + 3d, \\; \\ldots, \\; a + (n-1)d\\)<\/strong><\/p><p><span style=\"font-weight: 400;\">Here:<\/span><\/p><ul><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">a<\/span><span style=\"font-weight: 400;\"> = first term<\/span><span style=\"font-weight: 400;\"><br \/><\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">d<\/span><span style=\"font-weight: 400;\"> = common difference<\/span><span style=\"font-weight: 400;\"><br \/><\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">n<\/span><span style=\"font-weight: 400;\"> = number of terms<\/span><\/li><\/ul>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-a534078 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"a534078\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-0f11d35\" data-id=\"0f11d35\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-ebfdfe1 elementor-widget elementor-widget-text-editor\" data-id=\"ebfdfe1\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<h3><b><a id=\"4\"><\/a>nth Term of AP Formula<\/b><\/h3>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-1a1bd39 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"1a1bd39\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-8355baf\" data-id=\"8355baf\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-f5019d7 elementor-widget elementor-widget-image\" data-id=\"f5019d7\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-image\">\n\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"739\" height=\"492\" src=\"https:\/\/mp.moonpreneur.com\/math-corner\/wp-content\/uploads\/2025\/08\/types-of-arithmetic-progression.webp\" class=\"attachment-medium_large size-medium_large wp-image-36549\" alt=\"nth Term of AP Formula\" loading=\"lazy\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-f42c8cd elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"f42c8cd\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-90c4c1c\" data-id=\"90c4c1c\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-bd42b36 elementor-widget elementor-widget-text-editor\" data-id=\"bd42b36\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<p><span style=\"font-weight: 400;\">The formula for the nth term is: <b>\\(a_{n} = a + (n &#8211; 1) \\times d\\)<\/b><\/span><\/p><p><span style=\"font-weight: 400;\">Example: Find the 15th term of the AP: 3, 7, 11, 15, \u2026<\/span><\/p><ul><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">a = 3<\/span><span style=\"font-weight: 400;\">, <\/span><span style=\"font-weight: 400;\">d = 4<\/span><span style=\"font-weight: 400;\">, <\/span><span style=\"font-weight: 400;\">n = 15<\/span><span style=\"font-weight: 400;\"><br \/><\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">\\(a_{15} = 3 + (15 &#8211; 1) \\times 4 = 3 + 56 = 59\\)<\/span><\/li><\/ul><p><span style=\"font-weight: 400;\">So, the 15th term is <\/span><b>59<\/b><span style=\"font-weight: 400;\">.<\/span><\/p>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-79e3054 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"79e3054\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-d9aae39\" data-id=\"d9aae39\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-4fe2454 elementor-widget elementor-widget-text-editor\" data-id=\"4fe2454\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<h3><b><a id=\"5\"><\/a>Sum of n Terms Formula<\/b><\/h3>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-198b63d elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"198b63d\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-7997ecc\" data-id=\"7997ecc\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-c5109bc elementor-widget elementor-widget-text-editor\" data-id=\"c5109bc\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<p><span style=\"font-weight: 400;\">The sum of the first n terms of an AP is given by:<\/span><\/p>\\(S_{n} = \\frac{n}{2} \\big[2a + (n &#8211; 1) \\times d\\big]\\)<p><span style=\"font-weight: 400;\">Example: Find the sum of the first 20 terms of the AP: 7, 10, 13, \u2026<\/span><\/p><p><span style=\"font-weight: 400;\">Solution: a = 7, d = 3, n = 20<\/span><\/p>\\(S_{20} = \\frac{20}{2} \\big[2(7) + (20 &#8211; 1) \\times 3\\big] = 10[14 + 57] = 10 \\times 71 = 710\\)\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-bbe1cba elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"bbe1cba\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-207572e\" data-id=\"207572e\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-191493a elementor-widget elementor-widget-text-editor\" data-id=\"191493a\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<h3><b><a id=\"6\"><\/a>Types of Arithmetic Progression<\/b><\/h3>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-7dee117 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"7dee117\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-27d006d\" data-id=\"27d006d\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-a0b7053 elementor-widget elementor-widget-image\" data-id=\"a0b7053\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-image\">\n\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"739\" height=\"492\" src=\"https:\/\/mp.moonpreneur.com\/math-corner\/wp-content\/uploads\/2025\/08\/what-is-arithmetic-progression-AP.webp\" class=\"attachment-medium_large size-medium_large wp-image-36547\" alt=\"Types of Arithmetic Progression\" loading=\"lazy\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-cc266ef elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"cc266ef\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-b52118c\" data-id=\"b52118c\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-2bcad61 elementor-widget elementor-widget-text-editor\" data-id=\"2bcad61\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<p><b>Finite AP<\/b><span style=\"font-weight: 400;\"> \u2013 An AP with a limited number of terms.<\/span><span style=\"font-weight: 400;\"><br \/><\/span><span style=\"font-weight: 400;\"> Example: 5, 10, 15, 20 (ends at 20).<\/span><\/p><p><b>Infinite AP<\/b><span style=\"font-weight: 400;\"> \u2013 An AP that continues endlessly.<\/span><span style=\"font-weight: 400;\"><br \/><\/span><span style=\"font-weight: 400;\"> Example: 2, 4, 6, 8, \u2026<\/span><\/p>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-794775a elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"794775a\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-97b8a4f\" data-id=\"97b8a4f\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-5271173 elementor-widget elementor-widget-text-editor\" data-id=\"5271173\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<h3><b>List of AP Formulas<\/b><\/h3>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-69092eb elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"69092eb\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-c8213d4\" data-id=\"c8213d4\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-09aae3a elementor-widget elementor-widget-html\" data-id=\"09aae3a\" data-element_type=\"widget\" data-widget_type=\"html.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<p>Formulas of Arithmetic Progression (AP):<\/p>\n\n<table border=\"1\" cellpadding=\"8\" cellspacing=\"0\">\n  <thead>\n    <tr>\n      <th>Formula<\/th>\n      <th>Expression<\/th>\n    <\/tr>\n  <\/thead>\n  <tbody>\n    <tr>\n      <td>nth Term<\/td>\n      <td>\\(a_{n} = a + (n - 1)d\\)<\/td>\n    <\/tr>\n    <tr>\n      <td>Sum of n terms<\/td>\n      <td>\\(S_{n} = \\frac{n}{2} \\big[2a + (n - 1)d\\big]\\)<\/td>\n    <\/tr>\n    <tr>\n      <td>Sum when last term is known<\/td>\n      <td>\\(S_{n} = \\frac{n}{2} (a + l)\\)<\/td>\n    <\/tr>\n  <\/tbody>\n<\/table>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-e202c42 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"e202c42\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-538622b\" data-id=\"538622b\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-46abeba elementor-widget elementor-widget-text-editor\" data-id=\"46abeba\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<h3><b><a id=\"7\"><\/a>Examples and Solutions<\/b><\/h3>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-074e511 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"074e511\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-bb455bd\" data-id=\"bb455bd\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-b1cac90 elementor-widget elementor-widget-accordion\" data-id=\"b1cac90\" data-element_type=\"widget\" data-widget_type=\"accordion.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-accordion\">\n\t\t\t\t\t\t\t<div class=\"elementor-accordion-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-1861\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-1861\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon elementor-accordion-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-closed\"><i class=\"fas fa-plus\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-opened\"><i class=\"fas fa-minus\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-accordion-title\" tabindex=\"0\">Example 1 :<\/a>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<div id=\"elementor-tab-content-1861\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-1861\"><p><span style=\"font-weight: 400;\">Find the value of n if a = 2, d = 5, and an = 52.<\/span><\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<div class=\"elementor-accordion-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-1862\" class=\"elementor-tab-title\" data-tab=\"2\" role=\"button\" aria-controls=\"elementor-tab-content-1862\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon elementor-accordion-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-closed\"><i class=\"fas fa-plus\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-opened\"><i class=\"fas fa-minus\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-accordion-title\" tabindex=\"0\">Solution : <\/a>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<div id=\"elementor-tab-content-1862\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"2\" role=\"region\" aria-labelledby=\"elementor-tab-title-1862\"><ul>\n<li>\\(a_{n} = a + (n &#8211; 1) \\times d\\)<\/li>\n<li>\\(52 = 2 + (n &#8211; 1) \\times 5\\)<\/li>\n<li>\\(n = 11\\)<\/li><\/ul><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-7f88c85\" data-id=\"7f88c85\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-1a2f99b elementor-widget elementor-widget-accordion\" data-id=\"1a2f99b\" data-element_type=\"widget\" data-widget_type=\"accordion.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-accordion\">\n\t\t\t\t\t\t\t<div class=\"elementor-accordion-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-2741\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-2741\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon elementor-accordion-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-closed\"><i class=\"fas fa-plus\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-opened\"><i class=\"fas fa-minus\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-accordion-title\" tabindex=\"0\">Example 2 :<\/a>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<div id=\"elementor-tab-content-2741\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-2741\"><p><span style=\"font-weight: 400;\">\u00a0Find the 15th term of the AP: 7, 11, 15, \u2026<\/span><\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<div class=\"elementor-accordion-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-2742\" class=\"elementor-tab-title\" data-tab=\"2\" role=\"button\" aria-controls=\"elementor-tab-content-2742\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon elementor-accordion-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-closed\"><i class=\"fas fa-plus\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-opened\"><i class=\"fas fa-minus\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-accordion-title\" tabindex=\"0\">Solution : <\/a>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<div id=\"elementor-tab-content-2742\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"2\" role=\"region\" aria-labelledby=\"elementor-tab-title-2742\"><ul>\n<li><span style=\"font-weight: 400;\">\\(a_{n} = 7 + (15 &#8211; 1) \\times 4\\)<br \/><\/span><\/li>\n<li>\\(a_{n} = 7 + 56\\)<\/li>\n<li>\\(a_{n} = 63\\)<\/li>\n<\/ul><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-4d7645f elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"4d7645f\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-7ca67cd\" data-id=\"7ca67cd\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-23e21e9 elementor-widget elementor-widget-text-editor\" data-id=\"23e21e9\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<h3><b><a id=\"8\"><\/a>Practice Problems<\/b><\/h3>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-d20be71 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"d20be71\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-b764155\" data-id=\"b764155\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-a4b869f elementor-widget elementor-widget-text-editor\" data-id=\"a4b869f\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<ol><li><span style=\"font-weight: 400;\"> Find the 12th term of the AP: 5, 9, 13, \u2026<\/span><\/li><li><span style=\"font-weight: 400;\"> If a = 3, d = 7, and n = 25, find \\(S_{n}\\)<br \/><\/span><\/li><li><span style=\"font-weight: 400;\"> Find the common difference if the 6th term is 29 and the 10th term is 45.<\/span><\/li><\/ol>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-adc3f0e elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"adc3f0e\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-ab070e3\" data-id=\"ab070e3\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-71a30b5 elementor-widget elementor-widget-text-editor\" data-id=\"71a30b5\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<h3><b>Conclusion<\/b><\/h3>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-46b656c elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"46b656c\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-1f0f337\" data-id=\"1f0f337\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-784f8f2 elementor-widget elementor-widget-text-editor\" data-id=\"784f8f2\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<p><span style=\"font-weight: 400;\">Arithmetic Progression (AP) is one of the most fundamental concepts in mathematics that builds a strong foundation for higher studies in algebra and sequences. By understanding its definition, formulas, and real-life applications, students can easily solve problems related to patterns, series, and progressions. Whether it\u2019s calculating the nth term or finding the sum of terms, mastering AP helps sharpen logical thinking and problem-solving skills, making it a vital part of learning mathematics.<\/span><\/p><p><span style=\"font-weight: 400;\">Want to spark your child\u2019s interest in math and boost their skills? Moonpreneur&#8217;s online math curriculum stands out because it engages kids with hands-on lessons, helps them apply math in real-life situations, and makes learning math exciting!<\/span><\/p><p><span style=\"font-weight: 400;\">You can opt for our <\/span><a href=\"https:\/\/moonpreneur.com\/innovator-program\/advanced-math\/\"><span style=\"font-weight: 400;\">Advanced Math<\/span><\/a><span style=\"font-weight: 400;\"> or Vedic Math+Mental Math courses. Our <\/span><a href=\"https:\/\/mp.moonpreneur.com\/math-quiz-for-kids\/\"><span style=\"font-weight: 400;\">Math Quiz<\/span><\/a><span style=\"font-weight: 400;\"> for grades 3rd, 4th, 5th, and 6th helps in further exciting and engaging in mathematics with hands-on lessons.<\/span><\/p>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-1a34aa4 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"1a34aa4\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-7253a55\" data-id=\"7253a55\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-9f48ab5 elementor-widget elementor-widget-text-editor\" data-id=\"9f48ab5\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<h4><b>Related Blogs:<\/b><\/h4>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-aabbae4 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"aabbae4\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-f16bb1d\" data-id=\"f16bb1d\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-175177d elementor-widget elementor-widget-text-editor\" data-id=\"175177d\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<ul><li style=\"font-weight: 400;\" aria-level=\"1\"><h6><a href=\"https:\/\/mp.moonpreneur.com\/math-corner\/step-deviation-method\/\"><span style=\"font-weight: 400;\">Step Deviation Method in Statistics \u2013 Definition, Formula, and Solved Example<\/span><\/a><\/h6><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><h6><a href=\"https:\/\/mp.moonpreneur.com\/math-corner\/frequency-formula\/\"><span style=\"font-weight: 400;\">What is the Frequency Formula? Definition, Examples, and Related Equations<\/span><\/a><\/h6><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><h6><a href=\"https:\/\/mp.moonpreneur.com\/math-corner\/sat-essay\/\"><span style=\"font-weight: 400;\">What Is the SAT Essay? Everything You Need to Know<\/span><\/a><\/h6><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><h6><a href=\"https:\/\/mp.moonpreneur.com\/math-corner\/sat-math-sections\/\"><span style=\"font-weight: 400;\">An overview of the SAT Math Test Sections<\/span><\/a><\/h6><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><h6><a href=\"https:\/\/mp.moonpreneur.com\/math-corner\/sat-superscore\/\"><span style=\"font-weight: 400;\">SAT Superscore: What It Is and Why It Matters?<\/span><\/a><\/h6><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><h6><a href=\"https:\/\/mp.moonpreneur.com\/math-corner\/mean-median-mode\/\"><span style=\"font-weight: 400;\">Mean vs. Median vs. Mode: What is the Difference?<\/span><\/a><\/h6><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><h6><a href=\"https:\/\/mp.moonpreneur.com\/math-corner\/mathway-reviewed\/\"><span style=\"font-weight: 400;\">Mathway Reviewed: Pros, Cons, and Everything You Need to Know<\/span><\/a><\/h6><\/li><\/ul>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-ea825f6 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"ea825f6\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-9005678\" data-id=\"9005678\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-d1a3d8e elementor-widget elementor-widget-text-editor\" data-id=\"d1a3d8e\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<h3><b><a id=\"9\"><\/a>FAQs on Arithmetic Progression<\/b><\/h3>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-9ab6533 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"9ab6533\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-c864211\" data-id=\"c864211\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-c689ff8 elementor-widget elementor-widget-toggle\" data-id=\"c689ff8\" data-element_type=\"widget\" data-widget_type=\"toggle.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-toggle\">\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-2081\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-2081\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon elementor-toggle-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-closed\"><i class=\"fas fa-caret-right\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-opened\"><i class=\"elementor-toggle-icon-opened fas fa-caret-up\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-toggle-title\" tabindex=\"0\">Q1: What is the formula for the nth term of AP?<\/a>\n\t\t\t\t\t<\/div>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-2081\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-2081\"><p><span style=\"font-weight: 400;\">Answer: \\(a_{n} = a + (n &#8211; 1) \\times d\\)<br \/><\/span><\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-2082\" class=\"elementor-tab-title\" data-tab=\"2\" role=\"button\" aria-controls=\"elementor-tab-content-2082\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon elementor-toggle-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-closed\"><i class=\"fas fa-caret-right\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-opened\"><i class=\"elementor-toggle-icon-opened fas fa-caret-up\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-toggle-title\" tabindex=\"0\">Q2: How do you calculate the sum of an AP?<\/a>\n\t\t\t\t\t<\/div>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-2082\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"2\" role=\"region\" aria-labelledby=\"elementor-tab-title-2082\"><p><span style=\"font-weight: 400;\">Answer: \\(S_{n} = \\frac{n}{2} \\big[2a + (n &#8211; 1) \\times d\\big]\\)<br \/><\/span><\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<div class=\"elementor-toggle-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-2083\" class=\"elementor-tab-title\" data-tab=\"3\" role=\"button\" aria-controls=\"elementor-tab-content-2083\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon elementor-toggle-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-closed\"><i class=\"fas fa-caret-right\"><\/i><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-toggle-icon-opened\"><i class=\"elementor-toggle-icon-opened fas fa-caret-up\"><\/i><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-toggle-title\" tabindex=\"0\">Q3: Can the common difference be negative?<\/a>\n\t\t\t\t\t<\/div>\n\n\t\t\t\t\t<div id=\"elementor-tab-content-2083\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"3\" role=\"region\" aria-labelledby=\"elementor-tab-title-2083\"><p><span style=\"font-weight: 400;\">Answer: Yes, if d &lt; 0, the sequence decreases with each term.<\/span><\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Introduction Arithmetic Progression (AP) is one of the most important concepts in mathematics. It represents a sequence of numbers where the difference between consecutive terms remains constant. This simple yet powerful idea is widely used in mathematics, physics, finance, and even in our daily lives. Table of Contents What is Arithmetic Progression (AP)? \u00a0Standard Notation [&hellip;]<\/p>\n","protected":false},"author":116,"featured_media":36550,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false},"categories":[969,1035],"tags":[],"acf":[],"_links":{"self":[{"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/posts\/36546"}],"collection":[{"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/users\/116"}],"replies":[{"embeddable":true,"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/comments?post=36546"}],"version-history":[{"count":85,"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/posts\/36546\/revisions"}],"predecessor-version":[{"id":36651,"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/posts\/36546\/revisions\/36651"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/media\/36550"}],"wp:attachment":[{"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/media?parent=36546"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/categories?post=36546"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/tags?post=36546"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}