{"id":136,"date":"2022-04-13T10:06:32","date_gmt":"2022-04-13T10:06:32","guid":{"rendered":"http:\/\/10thclass.deltapublications.in\/?page_id=136"},"modified":"2025-03-05T11:46:59","modified_gmt":"2025-03-05T11:46:59","slug":"g-3-write-variable-expressions-for-arithmetic-sequences","status":"publish","type":"page","link":"https:\/\/10thclass.deltapublications.in\/index.php\/g-3-write-variable-expressions-for-arithmetic-sequences\/","title":{"rendered":"G.3 Write variable expressions for arithmetic sequences"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color has-large-font-size\" style=\"color:#00056d;text-transform:uppercase\"><strong>Write variable expressions for arithmetic sequences<\/strong><\/h2>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-8575bb3b3b80298a7cd0940fe3fcb3bb\" style=\"color:#74008b;text-transform:capitalize\"><strong>key notes:<\/strong><\/p>\n\n\n\n<p class=\"has-large-font-size\"><strong>Arithmetic Sequence<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. This difference is called the <strong>common difference<\/strong> (denoted as d).<\/li>\n\n\n\n<li><strong>Example<\/strong>: 2,5,8,11,\u2026(common difference d=3.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-large-font-size\"><strong>General Form<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>The n-th term of an arithmetic sequence can be expressed using the formula: a<sub>n<\/sub>=a<sub>1<\/sub>+(n\u22121)d<\/li>\n<\/ul>\n\n\n\n<p class=\"has-large-font-size\"><strong>Where:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>a<sub>n\u200b <\/sub>= the n-th term<\/li>\n\n\n\n<li>a<sub>1<\/sub> = 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-large-font-size\"><strong>Example Expression<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>For a sequence starting with 4 and having a common difference of 3:\n<ul class=\"wp-block-list\">\n<li>a<sub>1<\/sub>=4<\/li>\n\n\n\n<li>d=3<\/li>\n\n\n\n<li>The expression for the n-th term: <\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center has-large-font-size\">a<sub>n\u200b<\/sub>=4+(n\u22121)\u22c53<\/p>\n\n\n\n<p class=\"has-large-font-size\"><strong>Simplifying gives: <\/strong>   a<sub>n<\/sub>=3n+1<\/p>\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-a87780673aa8a78a58620ce38de54a13\" style=\"background-color:#f5f6c1\"><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-59fd71284de45e2349cd411f2e3225cb\"><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 has-large-font-size wp-elements-0458b514a2dbe05dc3f2ca9200bc332e\" style=\"color:#b00012\">\ud83d\udd14 Write an expression to describe the sequence below. <\/p>\n\n\n\n<p>Use&nbsp;<em>n<\/em>&nbsp;to represent the position of a term in the sequence, where&nbsp;<em>n<\/em>&nbsp;= 1&nbsp;for the first term.<\/p>\n\n\n\n<p>-16,&nbsp;-15,&nbsp;-14,&nbsp;-13, &#8230;<\/p>\n<\/div><\/div>\n\n\n\n<p>The sequence&nbsp;-16,&nbsp;-15,&nbsp;-14,&nbsp;-13, &#8230; looks like 1, 2, 3, 4, &#8230; except each term is 17 smaller. So, the expression that describes the sequence is&nbsp;<strong><em>n<\/em>&nbsp;\u2212 17<\/strong>. Check the first four terms:<\/p>\n\n\n\n<p>To find the 1st term, plug in n = 1.<\/p>\n\n\n\n<p>n \u2212 17 = 1 \u2212 17 = \u201316<\/p>\n\n\n\n<p>To find the 2nd term, plug in n = 2.<\/p>\n\n\n\n<p>n \u2212 17 = 2 \u2212 17 = \u201315<\/p>\n\n\n\n<p>To find the 3rd term, plug-in n = 3.<\/p>\n\n\n\n<p>n \u2212 17 = 3 \u2212 17 = \u201314<\/p>\n\n\n\n<p>To find the 4th term, plug-in n = 4.<\/p>\n\n\n\n<p>n \u2212 17 = 4 \u2212 17 = \u201313<\/p>\n\n\n\n<p>The sequence \u201316, \u201315, \u201314, \u201313, \u2026 is described by the expression n \u2212 17.<\/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-3f62ccc466a37a7402c11d7dd2d914e0\" style=\"background-color:#dbf9dc\"><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-c77b541b2d61a5ca30e64c2246a42b64\"><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-4961f11d4d8e47451f727b6969df5a86\" style=\"color:#b00012\">\ud83d\udd14 Write an expression to describe the sequence below.<\/p>\n\n\n\n<p> Use&nbsp;<em>n<\/em>&nbsp;to represent the position of a term in the sequence, where&nbsp;<em>n<\/em>&nbsp;= 1&nbsp;for the first term.<\/p>\n\n\n\n<p>-2,&nbsp;-4,&nbsp;-6,&nbsp;-8, &#8230;<\/p>\n<\/div><\/div>\n\n\n\n<p>The sequence&nbsp;-2,&nbsp;-4,&nbsp;-6,&nbsp;-8, &#8230; looks like 1, 2, 3, 4, &#8230; except each term is multiplied by&nbsp;<sup>\u2013<\/sup>2. So, the expression that describes the sequence is&nbsp;<strong><sup>\u2013<\/sup>2<em>n<\/em><\/strong>, where&nbsp;<em>n<\/em>&nbsp;represents the position of a term in the sequence. Check the first four terms:<\/p>\n\n\n\n<p>To find the 1st term, plug in n = 1.<\/p>\n\n\n\n<p>\u20132n = \u20132(1) = \u20132<\/p>\n\n\n\n<p>To find the 2nd term, plug in n = 2.<\/p>\n\n\n\n<p>\u20132n = \u20132(2) = \u20134<\/p>\n\n\n\n<p>To find the 3rd term, plug-in n = 3.<\/p>\n\n\n\n<p>\u20132n = \u20132(3) = \u20136<\/p>\n\n\n\n<p>To find the 4th term, plug-in n = 4.<\/p>\n\n\n\n<p>\u20132n = \u20132(4) = \u20138<\/p>\n\n\n\n<p>The sequence \u20132, \u20134, \u20136, \u20138, \u2026 is described by the expression \u20132n.<\/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-ff5fa4e518a6b36d68f07174b69772a8\" style=\"background-color:#dddaf9\"><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-d141dc85d78813752a26269b5447f06f\"><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-881f301c6c460133b8bdd0855b5f56ca\" style=\"color:#b00012\">\ud83d\udd14 Write an expression to describe the sequence below. <\/p>\n\n\n\n<p>Use&nbsp;<em>n<\/em>&nbsp;to represent the position of a term in the sequence, where&nbsp;<em>n<\/em>&nbsp;= 1&nbsp;for the first term.<\/p>\n\n\n\n<p>58, 59, 60, 61, &#8230;<\/p>\n<\/div><\/div>\n\n\n\n<p>The sequence 58, 59, 60, 61, &#8230; looks like 1, 2, 3, 4, &#8230; except each term is 57 larger. So, the expression that describes the sequence is&nbsp;<strong><em>n<\/em>&nbsp;+ 57<\/strong>. Check the first four terms:<\/p>\n\n\n\n<p>To find the 1st term, plug in n = 1.<\/p>\n\n\n\n<p>n + 57 = 1 + 57 = 58<\/p>\n\n\n\n<p>To find the 2nd term, plug in n = 2.<\/p>\n\n\n\n<p>n + 57 = 2 + 57 = 59<\/p>\n\n\n\n<p>To find the 3rd term, plug-in n = 3.<\/p>\n\n\n\n<p>n + 57 = 3 + 57 = 60<\/p>\n\n\n\n<p>To find the 4th term, plug-in n = 4.<\/p>\n\n\n\n<p>n + 57 = 4 + 57 = 61<\/p>\n\n\n\n<p>The sequence 58, 59, 60, 61, \u2026 is described by the expression n + 57.<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#d90000\">let&#8217;s practice!\ud83d\udd8a\ufe0f<\/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\/79951\/598\/467\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-28.png\" alt=\"\" class=\"wp-image-6816\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-28.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-28-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-28-150x150.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\/79562\/753\/307\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-46.png\" alt=\"\" class=\"wp-image-6817\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-46.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-46-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-46-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Write variable expressions for arithmetic sequences key notes: Arithmetic Sequence: General Form: Where: Example Expression: an\u200b=4+(n\u22121)\u22c53 Simplifying gives: an=3n+1 Learn with an example \ud83d\udd14 Write an expression to describe the sequence below. Use&nbsp;n&nbsp;to represent the position of a term in the sequence, where&nbsp;n&nbsp;= 1&nbsp;for the first term. -16,&nbsp;-15,&nbsp;-14,&nbsp;-13, &#8230; The sequence&nbsp;-16,&nbsp;-15,&nbsp;-14,&nbsp;-13, &#8230; looks like 1,<a class=\"more-link\" href=\"https:\/\/10thclass.deltapublications.in\/index.php\/g-3-write-variable-expressions-for-arithmetic-sequences\/\">Continue reading <span class=\"screen-reader-text\">&#8220;G.3 Write 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-136","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/136","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=136"}],"version-history":[{"count":21,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/136\/revisions"}],"predecessor-version":[{"id":17606,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/136\/revisions\/17606"}],"wp:attachment":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=136"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}