{"id":134,"date":"2022-04-13T10:06:05","date_gmt":"2022-04-13T10:06:05","guid":{"rendered":"http:\/\/10thclass.deltapublications.in\/?page_id=134"},"modified":"2025-03-05T11:46:38","modified_gmt":"2025-03-05T11:46:38","slug":"g-2-evaluate-variable-expressions-for-arithmetic-sequences","status":"publish","type":"page","link":"https:\/\/10thclass.deltapublications.in\/index.php\/g-2-evaluate-variable-expressions-for-arithmetic-sequences\/","title":{"rendered":"G.2 Evaluate variable expressions for arithmetic sequences"},"content":{"rendered":"\n<h4 class=\"wp-block-heading has-text-align-center has-text-color has-huge-font-size\" style=\"color:#00056d;text-transform:uppercase\"><strong>Evaluate variable expressions for arithmetic sequences<\/strong><\/h4>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-9eab8b80198ef55bc96d653fd9da2182\" style=\"color:#74008b;text-transform:uppercase\"><strong>key notes:<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">1. <strong>Understanding Arithmetic Sequences<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>An <strong>arithmetic sequence<\/strong> is a sequence of numbers in which the difference between consecutive terms is constant. This difference is called the <strong>common difference (d)<\/strong>.<\/li>\n\n\n\n<li>The general form of an arithmetic sequence can be expressed as: a<sub>n<\/sub>=a<sub>1<\/sub>+(n\u22121)\u22c5d<\/li>\n<\/ul>\n\n\n\n<p class=\"has-large-font-size\">where:<\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>a<sub>n<\/sub> = the nth term of the sequence<\/li>\n\n\n\n<li>a<sub>1<\/sub>\u200b = the first term of the sequence<\/li>\n\n\n\n<li>n = the term number<\/li>\n\n\n\n<li>d = common difference<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center has-text-color has-large-font-size\" style=\"color:#105000\"><strong>Learn with an example<\/strong><\/p>\n\n\n\n<div class=\"wp-block-group has-primary-color has-text-color has-background has-link-color has-large-font-size wp-elements-66f15191070da15a29f1516ffd4ced8f\" style=\"background-color:#9bf2a8\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-primary-color has-background-background-color has-text-color has-background has-link-color wp-elements-99604ff344d76872a84e7ff9fb053877\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color has-link-color wp-elements-41a8a05b53209dbcbcf1a0d11ad6c496\" style=\"color:#b00012\">\ud83d\udd14 Find the first three terms of the sequence defined below, where&nbsp;<em>n<\/em>&nbsp;represents the position of a term in the sequence. Start with&nbsp;<em>n<\/em>&nbsp;= 1.<\/p>\n\n\n\n<p>-7<em>n<\/em>&nbsp;+ 3<\/p>\n\n\n\n<p>____ ,____&nbsp;,____<\/p>\n<\/div><\/div>\n\n\n\n<p>To find the 1<sup>st<\/sup>&nbsp;term, plug in&nbsp;<em>n<\/em>&nbsp;= 1.<\/p>\n\n\n\n<p>-7n + 3 = -7(1) + 3 = -7 + 3 = -4<\/p>\n\n\n\n<p>To find the 2<sup>nd<\/sup>&nbsp;term, plug in&nbsp;<em>n<\/em>&nbsp;= 2.<\/p>\n\n\n\n<p>-7n + 3 = -7(2) + 3 = -14 + 3 = -11<\/p>\n\n\n\n<p>To find the 3<sup>rd<\/sup>&nbsp;term, plug-in&nbsp;<em>n<\/em>&nbsp;= 3.<\/p>\n\n\n\n<p>-7n + 3 = -7(3) + 3 = -21 + 3 = -18<\/p>\n\n\n\n<p>The first three terms of the sequence are -4, -11, -18.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-primary-color has-text-color has-background has-link-color has-large-font-size wp-elements-ec23df0305f5b685e6a939985232811c\" style=\"background-color:#f3d4a1\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-primary-color has-background-background-color has-text-color has-background has-link-color wp-elements-10aca38ac4be36c46a2ac791d34764a5\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color has-link-color wp-elements-f85fdf82ad2d8d5365946f4d2a48c4c6\" style=\"color:#b00012\">\ud83d\udd14 Find the first four terms of the sequence defined below, where&nbsp;<em>n<\/em>&nbsp;represents the position of a term in the sequence. Start with&nbsp;<em>n<\/em>&nbsp;= 1.<\/p>\n\n\n\n<p>10<em>n<\/em>&nbsp;+ 6<\/p>\n\n\n\n<p>____,____&nbsp;,____&nbsp;,____<\/p>\n<\/div><\/div>\n\n\n\n<p>To find the 1<sup>st<\/sup>&nbsp;term, plug in&nbsp;<em>n<\/em>&nbsp;= 1.<\/p>\n\n\n\n<p>10n + 6 = 10(1) + 6 = 10 + 6 = 16<\/p>\n\n\n\n<p>To find the 2<sup>nd<\/sup>&nbsp;term, plug in&nbsp;<em>n<\/em>&nbsp;= 2.<\/p>\n\n\n\n<p>10n + 6 = 10(2) + 6 = 20 + 6 = 26<\/p>\n\n\n\n<p>To find the 3<sup>rd<\/sup>&nbsp;term, plug-in&nbsp;<em>n<\/em>&nbsp;= 3.<\/p>\n\n\n\n<p>10n + 6 = 10(3) + 6 = 30 + 6 = 36<\/p>\n\n\n\n<p>To find the 4<sup>th<\/sup>&nbsp;term, plug-in&nbsp;<em>n<\/em>&nbsp;= 4.<\/p>\n\n\n\n<p>10n + 6 = 10(4) + 6 = 40 + 6 = 46<\/p>\n\n\n\n<p>The first four terms of the sequence are 16, 26, 36, 46.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-primary-color has-text-color has-background has-link-color has-large-font-size wp-elements-0c6f3d031343c5794257b0f06c6f059e\" style=\"background-color:#f9b0b0\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-primary-color has-background-background-color has-text-color has-background has-link-color wp-elements-ce3387448048476efc7217023340aade\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color has-link-color wp-elements-b77526aa07ec0d3b581f894b386ef8a9\" style=\"color:#b00012\">\ud83d\udd14 Find the first five terms of the sequence defined below, where&nbsp;<em>n<\/em>&nbsp;represents the position of a term in the sequence. Start with&nbsp;<em>n<\/em>&nbsp;= 1.<\/p>\n\n\n\n<p>6<em>n<\/em>&nbsp;+ 3<\/p>\n\n\n\n<p>____,____&nbsp;,____&nbsp;,____&nbsp;,____<\/p>\n<\/div><\/div>\n\n\n\n<p>To find the 1<sup>st<\/sup>&nbsp;term, plug in&nbsp;<em>n<\/em>&nbsp;= 1.<\/p>\n\n\n\n<p>6n + 3 = 6(1) + 3 = 6 + 3 = 9<\/p>\n\n\n\n<p>To find the 2<sup>nd<\/sup>&nbsp;term, plug in&nbsp;<em>n<\/em>&nbsp;= 2.<\/p>\n\n\n\n<p>6n + 3 = 6(2) + 3 = 12 + 3 = 15<\/p>\n\n\n\n<p>To find the 3<sup>rd<\/sup>&nbsp;term, plug-in&nbsp;<em>n<\/em>&nbsp;= 3.<\/p>\n\n\n\n<p>6n + 3 = 6(3) + 3 = 18 + 3 = 21<\/p>\n\n\n\n<p>To find the 4<sup>th<\/sup>&nbsp;term, plug-in&nbsp;<em>n<\/em>&nbsp;= 4.<\/p>\n\n\n\n<p>6n + 3 = 6(4) + 3 = 24 + 3 = 27<\/p>\n\n\n\n<p>To find the 5<sup>th<\/sup>&nbsp;term, plug-in&nbsp;<em>n<\/em>&nbsp;= 5.<\/p>\n\n\n\n<p>6n + 3 = 6(5) + 3 = 30 + 3 = 33<\/p>\n\n\n\n<p>The first five terms of the sequence are 9, 15, 21, 27, 33.<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#d90000\"><strong>let&#8217;s practice!\ud83d\udd8a\ufe0f<\/strong><\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/79950\/577\/516\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-26.png\" alt=\"\" class=\"wp-image-6802\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-26.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-26-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-26-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/79553\/106\/329\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-44.png\" alt=\"\" class=\"wp-image-6803\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-44.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-44-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-44-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Evaluate variable expressions for arithmetic sequences key notes: 1. Understanding Arithmetic Sequences where: Learn with an example \ud83d\udd14 Find the first three terms of the sequence defined below, where&nbsp;n&nbsp;represents the position of a term in the sequence. Start with&nbsp;n&nbsp;= 1. -7n&nbsp;+ 3 ____ ,____&nbsp;,____ To find the 1st&nbsp;term, plug in&nbsp;n&nbsp;= 1. -7n + 3 =<a class=\"more-link\" href=\"https:\/\/10thclass.deltapublications.in\/index.php\/g-2-evaluate-variable-expressions-for-arithmetic-sequences\/\">Continue reading <span class=\"screen-reader-text\">&#8220;G.2 Evaluate variable expressions for arithmetic sequences&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-134","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/134","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=134"}],"version-history":[{"count":23,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/134\/revisions"}],"predecessor-version":[{"id":17605,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/134\/revisions\/17605"}],"wp:attachment":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=134"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}