{"id":196173,"date":"2025-03-03T06:16:41","date_gmt":"2025-03-03T06:16:41","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=196173"},"modified":"2025-03-03T06:16:44","modified_gmt":"2025-03-03T06:16:44","slug":"for-each-sequence-determine-whether-it-appears-to-be-arithmetic-geometric-or-neither","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/03\/03\/for-each-sequence-determine-whether-it-appears-to-be-arithmetic-geometric-or-neither\/","title":{"rendered":"For each sequence, determine whether it appears to be arithmetic, geometric, or neither"},"content":{"rendered":"\n

For each sequence, determine whether it appears to be arithmetic, geometric, or neither. Arithmetic 128, 32, 8, 2, … Geometric Neither Arithmetic 4, 2, 1, 2, … Geometric Neither Arithmetic 6, 9, 12, 15, … Geometric Neither<\/p>\n\n\n\n

The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n

Let’s analyze each of the sequences you provided and determine whether they are arithmetic, geometric, or neither:<\/p>\n\n\n\n

    \n
  1. 128, 32, 8, 2, \u2026<\/strong><\/li>\n<\/ol>\n\n\n\n
      \n
    • Arithmetic<\/strong>: For a sequence to be arithmetic, the difference between each consecutive term must remain constant. Let’s check the differences:\n
        \n
      • 32 – 128 = -96<\/li>\n\n\n\n
      • 8 – 32 = -24<\/li>\n\n\n\n
      • 2 – 8 = -6<\/li>\n<\/ul>\n<\/li>\n\n\n\n
      • The differences are not constant, so this sequence is not arithmetic<\/strong>.<\/li>\n\n\n\n
      • Geometric<\/strong>: For a sequence to be geometric, each term must be obtained by multiplying the previous term by a constant ratio. Let’s check the ratios:\n
          \n
        • 32 \/ 128 = 0.25<\/li>\n\n\n\n
        • 8 \/ 32 = 0.25<\/li>\n\n\n\n
        • 2 \/ 8 = 0.25<\/li>\n<\/ul>\n<\/li>\n\n\n\n
        • The ratio is constant (0.25), so this sequence is geometric<\/strong>. Answer for the first sequence<\/strong>: Geometric<\/strong>.<\/li>\n<\/ul>\n\n\n\n
            \n
          1. 4, 2, 1, 2, \u2026<\/strong><\/li>\n<\/ol>\n\n\n\n
              \n
            • Arithmetic<\/strong>: Let’s check the differences:\n
                \n
              • 2 – 4 = -2<\/li>\n\n\n\n
              • 1 – 2 = -1<\/li>\n\n\n\n
              • 2 – 1 = 1<\/li>\n<\/ul>\n<\/li>\n\n\n\n
              • The differences are not constant, so this sequence is not arithmetic<\/strong>.<\/li>\n\n\n\n
              • Geometric<\/strong>: Let’s check the ratios:\n
                  \n
                • 2 \/ 4 = 0.5<\/li>\n\n\n\n
                • 1 \/ 2 = 0.5<\/li>\n\n\n\n
                • 2 \/ 1 = 2<\/li>\n<\/ul>\n<\/li>\n\n\n\n
                • The ratios are not constant, so this sequence is not geometric<\/strong>. Answer for the second sequence<\/strong>: Neither<\/strong>.<\/li>\n<\/ul>\n\n\n\n
                    \n
                  1. 6, 9, 12, 15, \u2026<\/strong><\/li>\n<\/ol>\n\n\n\n
                      \n
                    • Arithmetic<\/strong>: Let’s check the differences:\n
                        \n
                      • 9 – 6 = 3<\/li>\n\n\n\n
                      • 12 – 9 = 3<\/li>\n\n\n\n
                      • 15 – 12 = 3<\/li>\n<\/ul>\n<\/li>\n\n\n\n
                      • The differences are constant (3), so this sequence is arithmetic<\/strong>.<\/li>\n\n\n\n
                      • Geometric<\/strong>: Let’s check the ratios:\n
                          \n
                        • 9 \/ 6 = 1.5<\/li>\n\n\n\n
                        • 12 \/ 9 = 1.33 (approximately)<\/li>\n\n\n\n
                        • 15 \/ 12 = 1.25<\/li>\n<\/ul>\n<\/li>\n\n\n\n
                        • The ratios are not constant, so this sequence is not geometric<\/strong>. Answer for the third sequence<\/strong>: Arithmetic<\/strong>.<\/li>\n<\/ul>\n\n\n\n

                          Conclusion:<\/h3>\n\n\n\n
                            \n
                          • The first sequence (128, 32, 8, 2, \u2026) is geometric<\/strong>.<\/li>\n\n\n\n
                          • The second sequence (4, 2, 1, 2, \u2026) is neither<\/strong> arithmetic nor geometric.<\/li>\n\n\n\n
                          • The third sequence (6, 9, 12, 15, \u2026) is arithmetic<\/strong>.<\/li>\n<\/ul>\n\n\n\n

                            Now, let’s generate a visual representation of the sequences for better understanding.<\/p>\n\n\n\n

                            \"\"<\/figure>\n\n\n\n

                            Here is a visual representation of the three sequences. You can clearly see how the first sequence is geometric, the second sequence is neither arithmetic nor geometric, and the third sequence is arithmetic. Let me know if you’d like any more details!<\/p>\n","protected":false},"excerpt":{"rendered":"

                            For each sequence, determine whether it appears to be arithmetic, geometric, or neither. Arithmetic 128, 32, 8, 2, … Geometric Neither Arithmetic 4, 2, 1, 2, … Geometric Neither Arithmetic 6, 9, 12, 15, … Geometric Neither The Correct Answer and Explanation is : Let’s analyze each of the sequences you provided and determine whether […]<\/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-196173","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/196173","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=196173"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/196173\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=196173"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=196173"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=196173"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}