{"id":387,"date":"2022-04-13T05:02:46","date_gmt":"2022-04-13T05:02:46","guid":{"rendered":"http:\/\/8thclass.deltapublications.in\/?page_id=387"},"modified":"2026-03-23T04:59:13","modified_gmt":"2026-03-23T04:59:13","slug":"u-1-identify-arithmetic-and-geometric-sequences","status":"publish","type":"page","link":"https:\/\/8thclass.deltapublications.in\/index.php\/u-1-identify-arithmetic-and-geometric-sequences\/","title":{"rendered":"U.1 Identify arithmetic and geometric sequences"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong>Identify arithmetic and geometric sequences<\/strong><\/h2>\n\n\n\n<p class=\"has-text-color has-link-color has-huge-font-size wp-elements-4d4696560822e7cb72ec4be90d4370b1\" style=\"color:#74008b\">Key Notes:<\/p>\n\n\n\n<h1 class=\"wp-block-heading\">Sequences<\/h1>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading has-large-font-size\">\ud83d\udd22 What is a Sequence?<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>A <strong>sequence<\/strong> is a list of numbers arranged in a specific order.<\/li>\n\n\n\n<li>Each number in the sequence is called a <strong>term<\/strong>.<\/li>\n<\/ul>\n\n\n\n<p>\ud83d\udc49 Example: 2, 4, 6, 8, \u2026<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading has-large-font-size\">\u2795 Arithmetic Sequence (AP)<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>A sequence where the <strong>difference between consecutive terms is the same<\/strong>.<\/li>\n\n\n\n<li>This difference is called the <strong>common difference (d)<\/strong>.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">\ud83d\udccc Key Points:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Add the same number each time.<\/li>\n\n\n\n<li>Formula: <\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center\"><strong>Next\u00a0term = Previous\u00a0term + d<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Common difference: <\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center\"><strong>d = a<sub>2<\/sub> \u2212 a<sub>1<\/sub><\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">\u2705 Examples:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>3, 6, 9, 12 \u2192 (d = 3)<\/li>\n\n\n\n<li>10, 7, 4, 1 \u2192 (d = -3)<\/li>\n<\/ul>\n\n\n\n<p>\ud83d\udc49 <strong>Tip:<\/strong> If numbers increase or decrease by the same amount \u2192 Arithmetic<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading has-large-font-size\">\u2716\ufe0f Geometric Sequence (GP)<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>A sequence where each term is obtained by <strong>multiplying the previous term by the same number<\/strong>.<\/li>\n\n\n\n<li>This number is called the <strong>common ratio (r)<\/strong>.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">\ud83d\udccc Key Points:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Multiply by the same number each time.<\/li>\n\n\n\n<li>Formula: <\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center\"><strong>Next\u00a0term = Previous\u00a0term \u00d7 r<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Common ratio: <\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center\"><strong>r = a<sub>2<\/sub> \/ a<sub>1<\/sub><\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">\u2705 Examples:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>2, 4, 8, 16 \u2192 (r = 2)<\/li>\n\n\n\n<li>81, 27, 9, 3 \u2192 (r = 1\/3)<\/li>\n<\/ul>\n\n\n\n<p>\ud83d\udc49 <strong>Tip:<\/strong> If numbers grow or shrink by multiplying \u2192 Geometric<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading has-large-font-size\">\ud83d\udd0d How to Identify the Type<\/h2>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">Step 1:<\/h3>\n\n\n\n<p>Check the difference between terms:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Same difference \u2192 <strong>Arithmetic<\/strong><\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">Step 2:<\/h3>\n\n\n\n<p>Check the ratio between terms:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Same ratio \u2192 <strong>Geometric<\/strong><\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading has-large-font-size\">\u26a0\ufe0f Important Notes<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>A sequence <strong>cannot be both AP and GP<\/strong> (except special cases like constant sequences).<\/li>\n\n\n\n<li>If neither difference nor ratio is constant \u2192 <strong>Not AP or GP<\/strong><\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading has-large-font-size\">\ud83c\udfaf Quick Practice<\/h2>\n\n\n\n<p>Identify the type:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>5, 10, 15, 20 \u2192 ________<\/li>\n\n\n\n<li>3, 9, 27, 81 \u2192 ________<\/li>\n\n\n\n<li>7, 11, 16, 22 \u2192 ________<\/li>\n<\/ol>\n\n\n\n<p>\ud83d\udc49 Answers:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Arithmetic<\/li>\n\n\n\n<li>Geometric<\/li>\n\n\n\n<li>Neither<\/li>\n<\/ol>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading has-large-font-size\">\ud83d\udca1 Easy Memory Trick<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>AP \u2192 Add Pattern \u2795<\/strong><\/li>\n\n\n\n<li><strong>GP \u2192 Multiply Pattern \u2716\ufe0f<\/strong><\/li>\n<\/ul>\n\n\n\n<div class=\"wp-block-group has-large-font-size\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\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<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background\" style=\"background-color:#e5dfb9\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-large-font-size\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background\"><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-a2bf96f4f6310f40baf796493e6448eb\" style=\"color:#b00012\">\ud83c\udfaf Krysta is picking berries in the berry patch. She picks 36 berries from the first bush, 49 berries from the second bush, 64 berries from the third bush, and 81 berries from the fourth bush. What kind of sequence is this?<\/p>\n\n\n\n<p><strong>arithmetic       geometric     both          neither<\/strong><\/p>\n<\/div><\/div>\n\n\n\n<p>First, check if the sequence is arithmetic. There is not a constant difference between consecutive terms. So, the sequence is not arithmetic.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"700\" height=\"250\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/36-49-64-81-.....png\" alt=\"\" class=\"wp-image-7002\" style=\"width:325px;height:116px\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/36-49-64-81-.....png 700w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/36-49-64-81-....-300x107.png 300w\" sizes=\"auto, (max-width: 700px) 100vw, 700px\" \/><\/figure>\n\n\n\n<p>Next check if the sequence is geometric. There is not a constant multiplier between consecutive terms. So, the sequence is not geometric.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"700\" height=\"250\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/36-49-64-81-....-1.png\" alt=\"\" class=\"wp-image-7005\" style=\"width:367px;height:131px\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/36-49-64-81-....-1.png 700w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/36-49-64-81-....-1-300x107.png 300w\" sizes=\"auto, (max-width: 700px) 100vw, 700px\" \/><\/figure>\n\n\n\n<p>These multipliers are not all the same:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"700\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Add-a-heading-2.png\" alt=\"\" class=\"wp-image-7013\" style=\"width:258px;height:184px\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Add-a-heading-2.png 700w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Add-a-heading-2-300x214.png 300w\" sizes=\"auto, (max-width: 700px) 100vw, 700px\" \/><\/figure>\n\n\n\n<p>So, the sequence is neither arithmetic nor geometric.<\/p>\n<\/div><\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background\" style=\"background-color:#c8e9f1\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-large-font-size\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background\"><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-3f64fec257b5ca0e8a721f03771a2d0c\" style=\"color:#b00012\">\ud83c\udfaf <strong>Harper is organising her books and putting them on shelves. She put 218 books on the first shelf, 201 books on the second shelf, 184 books on the third shelf, and 167 books on the fourth shelf. What kind of sequence is this?<\/strong><\/p>\n\n\n\n<p><strong>arithmetic     geometric      both          neither<\/strong><\/p>\n<\/div><\/div>\n\n\n\n<p>First check if the sequence is arithmetic. There is a constant difference of&nbsp;<sup>&#8211;<\/sup>17 between consecutive terms. So, the sequence is arithmetic.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"100\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled__500___100px_-removebg-preview-1.png\" alt=\"\" class=\"wp-image-5839\" style=\"width:690px;height:138px\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled__500___100px_-removebg-preview-1.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled__500___100px_-removebg-preview-1-300x60.png 300w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure>\n\n\n\n<p>Next check if the sequence is geometric. There is not a constant multiplier between consecutive terms. So, the sequence is not geometric.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"100\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled__500___100px___1_-removebg-preview-1.png\" alt=\"\" class=\"wp-image-5840\" style=\"width:735px;height:147px\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled__500___100px___1_-removebg-preview-1.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled__500___100px___1_-removebg-preview-1-300x60.png 300w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure>\n\n\n\n<p>These multipliers are not all the same:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design-removebg-preview-1.png\" alt=\"\" class=\"wp-image-5841\" style=\"width:288px;height:288px\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design-removebg-preview-1.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design-removebg-preview-1-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design-removebg-preview-1-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure>\n\n\n\n<p>So, the sequence is only arithmetic.<\/p>\n<\/div><\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background\" style=\"background-color:#d3f1be\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-large-font-size\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background\"><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-385a315f4b5a11cbc932ac30a26bb8bc\" style=\"color:#b00012\"><strong>\ud83c\udfaf What kind of sequence is this?<\/strong><\/p>\n\n\n\n<p class=\"has-primary-color has-text-color has-link-color wp-elements-086e44cba116609ba368b9e2864d7c5d\">2, 3, 5, 8, &#8230;<br><strong>arithmetic       geometric        both       neither<\/strong><\/p>\n<\/div><\/div>\n\n\n\n<p>First check if the sequence is arithmetic. There is not a constant difference between consecutive terms. So, the sequence is not arithmetic.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"100\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled__500___100px___2_-removebg-preview.png\" alt=\"\" class=\"wp-image-5844\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled__500___100px___2_-removebg-preview.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled__500___100px___2_-removebg-preview-300x60.png 300w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure>\n\n\n\n<p>Next check if the sequence is geometric. There is not a constant multiplier between consecutive terms. So, the sequence is not geometric.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"100\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled__500___100px___3_-removebg-preview.png\" alt=\"\" class=\"wp-image-5845\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled__500___100px___3_-removebg-preview.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled__500___100px___3_-removebg-preview-300x60.png 300w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure>\n\n\n\n<p>These multipliers are not all the same:<\/p>\n\n\n\n<p>3\/2=1.5<\/p>\n\n\n\n<p>5\/3=1.667<\/p>\n\n\n\n<p>8\/5=1.6<\/p>\n\n\n\n<p>So, the sequence is neither arithmetic nor geometric.<\/p>\n<\/div><\/div>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#d90000\">let&#8217;s practice!<\/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\/109918\/254\/854\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Worksheet-1-2.png\" alt=\"\" class=\"wp-image-6989\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Worksheet-1-2.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Worksheet-1-2-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Worksheet-1-2-150x150.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\/31681\/132\/563\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Worksheet-1-1-1.png\" alt=\"\" class=\"wp-image-6990\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Worksheet-1-1-1.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Worksheet-1-1-1-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Worksheet-1-1-1-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Identify arithmetic and geometric sequences Key Notes: Sequences \ud83d\udd22 What is a Sequence? \ud83d\udc49 Example: 2, 4, 6, 8, \u2026 \u2795 Arithmetic Sequence (AP) \ud83d\udccc Key Points: Next\u00a0term = Previous\u00a0term + d d = a2 \u2212 a1 \u2705 Examples: \ud83d\udc49 Tip: If numbers increase or decrease by the same amount \u2192 Arithmetic \u2716\ufe0f Geometric Sequence<a class=\"more-link\" href=\"https:\/\/8thclass.deltapublications.in\/index.php\/u-1-identify-arithmetic-and-geometric-sequences\/\">Continue reading <span class=\"screen-reader-text\">&#8220;U.1 Identify arithmetic and geometric 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-387","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_hostinger_reach_plugin_has_subscription_block":false,"_hostinger_reach_plugin_is_elementor":false,"_links":{"self":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/387","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=387"}],"version-history":[{"count":26,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/387\/revisions"}],"predecessor-version":[{"id":22492,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/387\/revisions\/22492"}],"wp:attachment":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=387"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}