{"id":161943,"date":"2024-11-05T17:08:43","date_gmt":"2024-11-05T17:08:43","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=161943"},"modified":"2024-11-05T17:08:45","modified_gmt":"2024-11-05T17:08:45","slug":"is-the-following-an-arithmetic-sequence-geometric-sequence-or-neither","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/11\/05\/is-the-following-an-arithmetic-sequence-geometric-sequence-or-neither\/","title":{"rendered":"Is the following an arithmetic sequence, geometric sequence or neither"},"content":{"rendered":"\n<p>Is the following an arithmetic sequence, geometric sequence or neither: 324, 108, 36, 12, 4, \u2026<\/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>To determine whether the sequence 324, 108, 36, 12, 4 is an arithmetic sequence, a geometric sequence, or neither, we need to analyze the pattern of the numbers.<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Arithmetic Sequence<\/strong>: An arithmetic sequence is defined as a sequence in which the difference between consecutive terms is constant. To check if our sequence is arithmetic, we will calculate the differences between each pair of consecutive terms:<\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Difference between 324 and 108: ( 108 &#8211; 324 = -216 )<\/li>\n\n\n\n<li>Difference between 108 and 36: ( 36 &#8211; 108 = -72 )<\/li>\n\n\n\n<li>Difference between 36 and 12: ( 12 &#8211; 36 = -24 )<\/li>\n\n\n\n<li>Difference between 12 and 4: ( 4 &#8211; 12 = -8 ) The differences are: -216, -72, -24, and -8. Since the differences are not constant (they are decreasing and not equal), the sequence is <strong>not an arithmetic sequence<\/strong>.<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Geometric Sequence<\/strong>: A geometric sequence is defined as a sequence where the ratio between consecutive terms is constant. We can find the ratios of consecutive terms in our sequence:<\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Ratio between 324 and 108: ( \\frac{108}{324} = \\frac{1}{3} )<\/li>\n\n\n\n<li>Ratio between 108 and 36: ( \\frac{36}{108} = \\frac{1}{3} )<\/li>\n\n\n\n<li>Ratio between 36 and 12: ( \\frac{12}{36} = \\frac{1}{3} )<\/li>\n\n\n\n<li>Ratio between 12 and 4: ( \\frac{4}{12} = \\frac{1}{3} ) The ratios are all equal to ( \\frac{1}{3} ). Since the ratio between each pair of consecutive terms is constant, this sequence is classified as a <strong>geometric sequence<\/strong>.<\/li>\n<\/ul>\n\n\n\n<p>In conclusion, the sequence 324, 108, 36, 12, 4 is a geometric sequence with a common ratio of ( \\frac{1}{3} ). The constant ratio confirms that each term is obtained by multiplying the previous term by ( \\frac{1}{3} ). Thus, the correct answer is that it is a <strong>geometric sequence<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Is the following an arithmetic sequence, geometric sequence or neither: 324, 108, 36, 12, 4, \u2026 The Correct Answer and Explanation is: To determine whether the sequence 324, 108, 36, 12, 4 is an arithmetic sequence, a geometric sequence, or neither, we need to analyze the pattern of the numbers. In conclusion, the sequence 324, [&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-161943","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/161943","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=161943"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/161943\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=161943"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=161943"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=161943"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}