{"id":224147,"date":"2025-06-02T18:11:41","date_gmt":"2025-06-02T18:11:41","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=224147"},"modified":"2025-06-02T18:11:43","modified_gmt":"2025-06-02T18:11:43","slug":"find-the-missing-terms","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/02\/find-the-missing-terms\/","title":{"rendered":"find the missing terms"},"content":{"rendered":"\n

find the missing terms: 1) 2, 2, 4, 12, , <\/em><\/strong>. 2) 1, 2, 4, 8, , <\/em><\/strong>. 3) 1, 3, 9, 27, 81, _. 4) 1, 5, 25, 125,<\/strong><\/p>\n\n\n\n

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

1) Sequence: 2, 2, 4, 12, ___, ___<\/h3>\n\n\n\n

Let\u2019s look at the pattern:<\/p>\n\n\n\n

    \n
  • 2 \u2192 2 \u2192 4 \u2192 12<\/li>\n\n\n\n
  • Step 1: 2 \u2192 2 (\u00d71)<\/li>\n\n\n\n
  • Step 2: 2 \u2192 4 (\u00d72)<\/li>\n\n\n\n
  • Step 3: 4 \u2192 12 (\u00d73)<\/li>\n\n\n\n
  • Continuing this pattern:\n
      \n
    • Step 4: 12 \u00d7 4 = 48<\/strong><\/li>\n\n\n\n
    • Step 5: 48 \u00d7 5 = 240<\/strong><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n

      \u2705 Answer: 48, 240<\/strong><\/p>\n\n\n\n

      \n\n\n\n

      2) Sequence: 1, 2, 4, 8, ___, ___<\/h3>\n\n\n\n

      This is a geometric sequence where each term doubles the previous one:<\/p>\n\n\n\n

        \n
      • 1 \u2192 2 \u2192 4 \u2192 8<\/li>\n\n\n\n
      • Step 4: 8 \u00d7 2 = 16<\/strong><\/li>\n\n\n\n
      • Step 5: 16 \u00d7 2 = 32<\/strong><\/li>\n<\/ul>\n\n\n\n

        \u2705 Answer: 16, 32<\/strong><\/p>\n\n\n\n

        \n\n\n\n

        3) Sequence: 1, 3, 9, 27, 81, ___<\/h3>\n\n\n\n

        This is a geometric sequence where each term is multiplied by 3:<\/p>\n\n\n\n

          \n
        • 1 \u2192 3 \u2192 9 \u2192 27 \u2192 81<\/li>\n\n\n\n
        • Next: 81 \u00d7 3 = 243<\/strong><\/li>\n<\/ul>\n\n\n\n

          \u2705 Answer: 243<\/strong><\/p>\n\n\n\n

          \n\n\n\n

          4) Sequence: 1, 5, 25, 125, ___<\/h3>\n\n\n\n

          Another geometric sequence, each term is multiplied by 5:<\/p>\n\n\n\n

            \n
          • 1 \u2192 5 \u2192 25 \u2192 125<\/li>\n\n\n\n
          • Next: 125 \u00d7 5 = 625<\/strong><\/li>\n<\/ul>\n\n\n\n

            \u2705 Answer: 625<\/strong><\/p>\n\n\n\n

            \n\n\n\n

            Explanation<\/h3>\n\n\n\n

            Identifying numerical patterns involves recognizing either arithmetic or geometric progressions, or sometimes more complex rules. In the first sequence (2, 2, 4, 12…), we note that each number is multiplied by an increasing integer: \u00d71, \u00d72, \u00d73, and so on. Extending this gives us 12\u00d74 = 48, and then 48\u00d75 = 240. This progression illustrates a pattern where each term is the previous term multiplied by an incrementally increasing integer, common in factorial-related sequences.<\/p>\n\n\n\n

            The second sequence (1, 2, 4, 8…) is a simple geometric progression, where each term doubles. This type of sequence is often used to model exponential growth, such as population increase or compound interest, due to its consistent ratio.<\/p>\n\n\n\n

            The third sequence (1, 3, 9, 27, 81…) follows a geometric pattern with a common ratio of 3. These sequences grow faster than arithmetic ones and are a key concept in mathematics and computer science, especially in algorithm analysis and tree structures.<\/p>\n\n\n\n

            The fourth sequence (1, 5, 25, 125…) is also geometric, increasing by a factor of 5. Each term is 5n5^n, where nn increases by one at each step. Such exponential growth sequences emphasize how quickly values can escalate, illustrating the power of exponential functions.<\/p>\n\n\n\n

            In all cases, pattern recognition, especially geometric progressions, is crucial for mathematical reasoning and problem-solving.<\/p>\n\n\n\n

            \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

            find the missing terms: 1) 2, 2, 4, 12, , . 2) 1, 2, 4, 8, , . 3) 1, 3, 9, 27, 81, _. 4) 1, 5, 25, 125, The Correct Answer and Explanation is: 1) Sequence: 2, 2, 4, 12, ___, ___ Let\u2019s look at the pattern: \u2705 Answer: 48, 240 2) Sequence: […]<\/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-224147","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/224147","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=224147"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/224147\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=224147"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=224147"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=224147"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}