{"id":156231,"date":"2024-10-17T05:40:50","date_gmt":"2024-10-17T05:40:50","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=156231"},"modified":"2024-10-17T05:40:53","modified_gmt":"2024-10-17T05:40:53","slug":"write-a-recursive-definition-for-the-sequence-8-6-4-2","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/10\/17\/write-a-recursive-definition-for-the-sequence-8-6-4-2\/","title":{"rendered":"Write a recursive definition for the sequence 8, 6, 4, 2"},"content":{"rendered":"\n<p>Write a recursive definition for the sequence 8, 6, 4, 2, \u2026<br>(1 point)<br>A. a1\u200b=8;an\u200b=an\u22121\u200b\u22122<br>B. a\u2081 = 2;an-1 +6<br>C. a\u2081 = 8; an an-1 + 2<br>D. a\u2081 = 2; an an-1 +8<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>The correct recursive definition for the sequence 8, 6, 4, 2, \u2026 is:<\/p>\n\n\n\n<p><strong>( a_1 = 8; a_n = a_{n-1} &#8211; 2 )<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>This sequence starts at 8 and decreases by 2 at each step. To write a recursive definition, we need two parts:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Base case<\/strong>: This defines the first term of the sequence. In this case, the first term is ( a_1 = 8 ).<\/li>\n\n\n\n<li><strong>Recursive rule<\/strong>: This defines how each subsequent term relates to the previous one. In this sequence, every term is 2 less than the previous term. Hence, the recursive rule is ( a_n = a_{n-1} &#8211; 2 ).<\/li>\n<\/ol>\n\n\n\n<h4 class=\"wp-block-heading\">Analyzing the Other Options:<\/h4>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>( a_1 = 8; a_n = a_{n-1} &#8211; 2 )<\/strong>:<\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>This option is correct because it starts with 8 and subtracts 2 to get the next term, which matches the pattern of the sequence (8, 6, 4, 2, \u2026).<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>( a_1 = 2; a_n = a_{n-1} + 6 )<\/strong>:<\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>This is incorrect. Starting at 2 and adding 6 each time would result in a sequence like 2, 8, 14, 20, \u2026, which does not match the given sequence.<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>( a_1 = 8; a_n = a_{n-1} + 2 )<\/strong>:<\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>This is incorrect because adding 2 to each term would give a sequence like 8, 10, 12, \u2026, which does not fit the decreasing pattern.<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>( a_1 = 2; a_n = a_{n-1} + 8 )<\/strong>:<\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>This is incorrect because starting at 2 and adding 8 would result in 2, 10, 18, 26, \u2026, which again does not match the sequence.<\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">Recursive Sequences:<\/h4>\n\n\n\n<p>A recursive sequence defines each term based on its predecessor, using a specific rule. In this case, the rule is that each term is found by subtracting 2 from the previous term. Recursive sequences are useful because they break down complex patterns into simple, repeatable steps. For this problem, the correct answer follows a straightforward approach of starting from 8 and decreasing by 2, aligning with the recursive rule ( a_n = a_{n-1} &#8211; 2 ).<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Write a recursive definition for the sequence 8, 6, 4, 2, \u2026(1 point)A. a1\u200b=8;an\u200b=an\u22121\u200b\u22122B. a\u2081 = 2;an-1 +6C. a\u2081 = 8; an an-1 + 2D. a\u2081 = 2; an an-1 +8 The Correct Answer and Explanation is: The correct recursive definition for the sequence 8, 6, 4, 2, \u2026 is: ( a_1 = 8; a_n [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-156231","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/156231","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=156231"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/156231\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=156231"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=156231"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=156231"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}