{"id":290,"date":"2022-04-12T10:07:59","date_gmt":"2022-04-12T10:07:59","guid":{"rendered":"http:\/\/7thclass.deltapublications.in\/?page_id=290"},"modified":"2025-04-04T09:47:37","modified_gmt":"2025-04-04T09:47:37","slug":"o-1-identify-arithmetic-and-geometric-sequences","status":"publish","type":"page","link":"https:\/\/7thclass.deltapublications.in\/index.php\/o-1-identify-arithmetic-and-geometric-sequences\/","title":{"rendered":"O.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-huge-font-size\" style=\"color:#74008b\">Key notes:<\/p>\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>In an arithmetic sequence, there is a constant difference between consecutive terms. This means that you can always get from one term to the next by adding or subtracting the same number.<\/p>\n\n\n\n<p>In a geometric sequence, there is a constant multiplier between consecutive terms. This means that you can always get from one term to the next by multiplying or dividing by the same number.<\/p>\n\n\n\n<p>The only way a sequence can be both arithmetic and geometric is if it repeats the same number over and over again.<\/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-background\" style=\"background-color:#d2f6f8\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\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\" style=\"color:#b00012\">\ud83d\udc49 <strong>What kind of sequence is this?<\/strong><\/p>\n\n\n\n<p>16, 25, 36, 49, \u2026<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>arithmetic<\/li>\n\n\n\n<li>geometric<\/li>\n\n\n\n<li>both<\/li>\n\n\n\n<li>neither<\/li>\n<\/ul>\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<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"670\" height=\"200\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/01\/Untitled_design-removebg-preview-6.png\" alt=\"\" class=\"wp-image-4530\" style=\"width:395px;height:118px\" srcset=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/01\/Untitled_design-removebg-preview-6.png 670w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/01\/Untitled_design-removebg-preview-6-300x90.png 300w\" sizes=\"auto, (max-width: 670px) 100vw, 670px\" \/><\/figure><\/div>\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<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"670\" height=\"200\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/01\/Untitled_design__1_-removebg-preview-2.png\" alt=\"\" class=\"wp-image-4531\" style=\"width:476px;height:142px\" srcset=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/01\/Untitled_design__1_-removebg-preview-2.png 670w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/01\/Untitled_design__1_-removebg-preview-2-300x90.png 300w\" sizes=\"auto, (max-width: 670px) 100vw, 670px\" \/><\/figure><\/div>\n\n\n<p>These multipliers are not all the same:<\/p>\n\n\n\n<p>25 \/ 16 &nbsp;\u2248&nbsp;1.563<\/p>\n\n\n\n<p>36 \/ 25 =&nbsp;1.44<\/p>\n\n\n\n<p>49 \/ 36 \u2248&nbsp;1.361<\/p>\n\n\n\n<p>So, the sequence is neither arithmetic nor geometric.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background\" style=\"background-color:#dbd1f7\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\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\" style=\"color:#b00012\">\ud83d\udc49 <strong>On his mobile phone plan, Henry used 186 minutes in October, 198 minutes in November, 209 minutes in December, and 219 minutes in January. What kind of sequence is this?<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>arithmetic<\/li>\n\n\n\n<li>geometric<\/li>\n\n\n\n<li>both<\/li>\n\n\n\n<li>neither<\/li>\n<\/ul>\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<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"670\" height=\"200\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/01\/Untitled_design-removebg-preview-7.png\" alt=\"\" class=\"wp-image-4534\" style=\"width:402px;height:120px\" srcset=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/01\/Untitled_design-removebg-preview-7.png 670w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/01\/Untitled_design-removebg-preview-7-300x90.png 300w\" sizes=\"auto, (max-width: 670px) 100vw, 670px\" \/><\/figure><\/div>\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<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"670\" height=\"200\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/01\/Untitled_design__1_-removebg-preview-3.png\" alt=\"\" class=\"wp-image-4535\" style=\"width:446px;height:133px\" srcset=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/01\/Untitled_design__1_-removebg-preview-3.png 670w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/01\/Untitled_design__1_-removebg-preview-3-300x90.png 300w\" sizes=\"auto, (max-width: 670px) 100vw, 670px\" \/><\/figure><\/div>\n\n\n<p>These multipliers are not all the same:<\/p>\n\n\n\n<p>198 \/ 186 \u2248&nbsp;1.065<\/p>\n\n\n\n<p>209 \/ 198 \u2248&nbsp;1.056<\/p>\n\n\n\n<p>219 \/ 209 \u2248&nbsp;1.048<\/p>\n\n\n\n<p>So, the sequence is neither arithmetic nor geometric.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background\" style=\"background-color:#fef5e0\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\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\" style=\"color:#b00012\">\ud83d\udc49 <strong>What kind of sequence is this?<\/strong><\/p>\n\n\n\n<p>78, 87, 96, 105, \u2026<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>arithmetic<\/li>\n\n\n\n<li>geometric<\/li>\n\n\n\n<li>both<\/li>\n\n\n\n<li>neither<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<p>First check if the sequence is arithmetic. There is a constant difference of 9 between consecutive terms. So, the sequence is arithmetic.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"670\" height=\"200\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/01\/Untitled_design__2_-removebg-preview-3.png\" alt=\"\" class=\"wp-image-4536\" style=\"width:409px;height:122px\" srcset=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/01\/Untitled_design__2_-removebg-preview-3.png 670w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/01\/Untitled_design__2_-removebg-preview-3-300x90.png 300w\" sizes=\"auto, (max-width: 670px) 100vw, 670px\" \/><\/figure><\/div>\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<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"670\" height=\"200\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/01\/Untitled_design__3_-removebg-preview-2.png\" alt=\"\" class=\"wp-image-4537\" style=\"width:452px;height:135px\" srcset=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/01\/Untitled_design__3_-removebg-preview-2.png 670w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/01\/Untitled_design__3_-removebg-preview-2-300x90.png 300w\" sizes=\"auto, (max-width: 670px) 100vw, 670px\" \/><\/figure><\/div>\n\n\n<p>These multipliers are not all the same:<\/p>\n\n\n\n<p>87 \/ 78 \u2248&nbsp;1.115<\/p>\n\n\n\n<p>96 \/ 87 \u2248&nbsp;1.103<\/p>\n\n\n\n<p>105 \/ 96 \u2248&nbsp;1.094<\/p>\n\n\n\n<p>So, the sequence is only arithmetic.<\/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<\/div><\/div>\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\/89849\/551\/959\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-40.png\" alt=\"\" class=\"wp-image-6592\" srcset=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-40.png 500w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-40-300x300.png 300w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-40-150x150.png 150w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-40-400x400.png 400w\" 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\/31246\/691\/268\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-40.png\" alt=\"\" class=\"wp-image-6593\" srcset=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-40.png 500w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-40-300x300.png 300w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-40-150x150.png 150w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-40-400x400.png 400w\" 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: In an arithmetic sequence, there is a constant difference between consecutive terms. This means that you can always get from one term to the next by adding or subtracting the same number. In a geometric sequence, there is a constant multiplier between consecutive terms. This means that you<a class=\"more-link\" href=\"https:\/\/7thclass.deltapublications.in\/index.php\/o-1-identify-arithmetic-and-geometric-sequences\/\">Continue reading <span class=\"screen-reader-text\">&#8220;O.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,"footnotes":""},"class_list":["post-290","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/290","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=290"}],"version-history":[{"count":13,"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/290\/revisions"}],"predecessor-version":[{"id":15922,"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/290\/revisions\/15922"}],"wp:attachment":[{"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=290"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}