{"id":132,"date":"2022-04-13T10:05:41","date_gmt":"2022-04-13T10:05:41","guid":{"rendered":"http:\/\/10thclass.deltapublications.in\/?page_id=132"},"modified":"2025-07-31T11:04:05","modified_gmt":"2025-07-31T11:04:05","slug":"g-1-arithmetic-sequences","status":"publish","type":"page","link":"https:\/\/10thclass.deltapublications.in\/index.php\/g-1-arithmetic-sequences\/","title":{"rendered":"G.1 Arithmetic sequences"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00067d\"><strong>Arithmetic sequences<\/strong><\/h2>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-3a86f6ed3a54b3676f570e790fed15d9\" style=\"color:#74008b;text-transform:uppercase\"><strong>key notes:<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-dd0b27a2945445128bbf7c9fa28982a6\" style=\"color:#000060\"><strong>Arithmetic Sequences<\/strong><\/h3>\n\n\n\n<ol class=\"wp-block-list has-large-font-size\">\n<li><strong>Definition<\/strong>:\n<ul class=\"wp-block-list\">\n<li>An arithmetic sequence is a sequence of numbers in which the difference between any two consecutive terms is constant. This difference is called the <em>common difference<\/em> (d).<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>General Form<\/strong>: The n-th term of an arithmetic sequence can be expressed as:<\/li>\n<\/ol>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"338\" height=\"54\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/10\/image-2.png\" alt=\"\" class=\"wp-image-14193\" style=\"width:263px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/10\/image-2.png 338w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/10\/image-2-300x48.png 300w\" sizes=\"auto, (max-width: 338px) 100vw, 338px\" \/><\/figure><\/div>\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\u200b<\/sub> = n-th term<\/li>\n\n\n\n<li>a<sub>1\u200b<\/sub> = first term<\/li>\n\n\n\n<li>ddd = common difference<\/li>\n\n\n\n<li>n = term number<\/li>\n<\/ul>\n\n\n\n<p class=\"has-large-font-size\">3. <strong>Common Difference (d)<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>The common difference can be calculated as: d=a<sub>n<\/sub>\u2212a<sub>n\u22121<\/sub><\/li>\n\n\n\n<li>This can also be found by subtracting any two consecutive terms in the sequence.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-large-font-size\"><strong>4. Examples:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>For the sequence 2, 5, 8, 11, 14:\n<ul class=\"wp-block-list\">\n<li>First term a<sub>1<\/sub>=2<\/li>\n\n\n\n<li>Common difference d=3<\/li>\n\n\n\n<li>5th term a<sub>5<\/sub>=2+(5\u22121)\u00d73=14<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<p class=\"has-large-font-size\">5. <strong>Finding Specific Terms<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>To find a specific term in an arithmetic sequence, use the formula for a<sub>n<\/sub> with the values of a<sub>1<\/sub>,d, and n.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center has-text-color has-large-font-size\" style=\"color:#105000\">Learn with an example<\/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-a719bbdc4996ead35ee27c68f078128a\" style=\"background-color:#ecb3b3\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-primary-color has-background-background-color has-text-color has-background has-link-color wp-elements-6dcf71af94d423346b9c9693a8e41741\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color has-link-color wp-elements-08a9b15a06d68ab340bb8c7d6760ed5e\" style=\"color:#b00012\"><strong>Type the missing number in this sequence:<\/strong><\/p>\n\n\n\n<p>115, 108, 101,______, 87<br><\/p>\n<\/div><\/div>\n\n\n\n<p>First, look for a pattern. Notice how each number is 7 less than the previous number:<\/p>\n\n\n\n<p>115, 108, 101, __, 87<\/p>\n\n\n\n<p>To make the pattern complete, the number 94 must go in the blank space.<\/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-413a30468097acf59050642d12733bc0\" style=\"background-color:#cfeda4\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-primary-color has-background-background-color has-text-color has-background has-link-color wp-elements-cf4a69e82e9b09550e9671a17c428869\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color has-link-color wp-elements-85bb597af9af95fbe032fd59eb85878a\" style=\"color:#b00012\"><strong>Type the missing numbers in this sequence:<\/strong><\/p>\n\n\n\n<p>91, 85,______,______, 67, 61, 55<\/p>\n<\/div><\/div>\n\n\n\n<p>First, look for a pattern. Notice how each number is 6 less than the previous number:<\/p>\n\n\n\n<p>91,&nbsp;&nbsp;&nbsp;&nbsp;85,&nbsp;&nbsp;&nbsp;&nbsp;__,&nbsp;&nbsp;&nbsp;&nbsp;__,&nbsp;&nbsp;&nbsp;&nbsp;67,&nbsp;&nbsp;&nbsp;&nbsp;61,&nbsp;&nbsp;&nbsp;&nbsp;55<\/p>\n\n\n\n<p>To make the pattern complete, the numbers 79 and 73 must go in the blank spaces.<\/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-f34cf8e3f8fc937a1f2f667ac1682438\" style=\"background-color:#f4a4db\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-primary-color has-background-background-color has-text-color has-background has-link-color wp-elements-cc23607f1fe2907634313fdd9f5dc5d8\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color has-link-color wp-elements-08a9b15a06d68ab340bb8c7d6760ed5e\" style=\"color:#b00012\"><strong>Type the missing number in this sequence:<\/strong><\/p>\n\n\n\n<p>64, 74, 84, 94,____, 114<\/p>\n<\/div><\/div>\n\n\n\n<p>First, look for a pattern. Notice how each number is 10 more than the previous number:<\/p>\n\n\n\n<p>64, 74, 84, 94, __, 114<\/p>\n\n\n\n<p>To make the pattern complete, the number 104 must go in the blank space.<\/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:<\/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\/79948\/811\/437\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-27.png\" alt=\"\" class=\"wp-image-6807\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-27.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-27-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-27-150x150.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\/73861\/236\/864\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-45.png\" alt=\"\" class=\"wp-image-6808\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-45.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-45-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-45-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Arithmetic sequences key notes: Arithmetic Sequences Where: 3. Common Difference (d): 4. Examples: 5. Finding Specific Terms: Learn with an example Type the missing number in this sequence: 115, 108, 101,______, 87 First, look for a pattern. Notice how each number is 7 less than the previous number: 115, 108, 101, __, 87 To make<a class=\"more-link\" href=\"https:\/\/10thclass.deltapublications.in\/index.php\/g-1-arithmetic-sequences\/\">Continue reading <span class=\"screen-reader-text\">&#8220;G.1 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-132","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/132","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=132"}],"version-history":[{"count":31,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/132\/revisions"}],"predecessor-version":[{"id":18179,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/132\/revisions\/18179"}],"wp:attachment":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=132"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}