{"id":42713,"date":"2025-06-29T09:05:34","date_gmt":"2025-06-29T09:05:34","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=42713"},"modified":"2025-06-29T09:05:35","modified_gmt":"2025-06-29T09:05:35","slug":"the-given-sequence-is-not-a-geometric-sequence","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/the-given-sequence-is-not-a-geometric-sequence\/","title":{"rendered":"The given sequence is not a geometric sequence."},"content":{"rendered":"\n

. The given sequence is not a geometric sequence. Explanation: A geometric sequence is defined by a constant ratio between consecutive terms. In this case, the sequence is defined by the formula a_n = 6n^2 + 5. To check if it’s geometric, we need to see if the ratio of consecutive terms is constant. Let’s take two consecutive terms, for example, a_1 and a_2: a_1 = 6(1)^2 + 5 = 6 + 5 = 11 a_2 = 6(2)^2 + 5 = 6(4) + 5 = 24 + 5 = 29 The ratio of a_2 to a_1 is: r = a_2 \/ a_1 = 29 \/ 11 Now let’s take a_2 and a_3: a_3 = 6(3)^2 + 5 = 6(9) + 5 = 54 + 5 = 59 The ratio of a_3 to a_2 is: r = a_3 \/ a_2 = 59 \/ 29 Since the ratio between consecutive terms is not constant (29\/11 \u2260 59\/29), the sequence is not geometric. Therefore, the correct answer is C.<\/p>\n\n\n\n

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

The given sequence is defined by the formula an=6n2+5a_n = 6n^2 + 5an\u200b=6n2+5, where nnn is the term number. To determine whether this sequence is a geometric sequence, we need to check if the ratio between consecutive terms is constant.<\/p>\n\n\n\n

Step-by-Step Process:<\/h3>\n\n\n\n
    \n
  1. Find the first few terms<\/strong> of the sequence:\n
      \n
    • For n=1n = 1n=1: a1=6(1)2+5=6+5=11a_1 = 6(1)^2 + 5 = 6 + 5 = 11a1\u200b=6(1)2+5=6+5=11<\/li>\n\n\n\n
    • For n=2n = 2n=2: a2=6(2)2+5=6(4)+5=24+5=29a_2 = 6(2)^2 + 5 = 6(4) + 5 = 24 + 5 = 29a2\u200b=6(2)2+5=6(4)+5=24+5=29<\/li>\n\n\n\n
    • For n=3n = 3n=3: a3=6(3)2+5=6(9)+5=54+5=59a_3 = 6(3)^2 + 5 = 6(9) + 5 = 54 + 5 = 59a3\u200b=6(3)2+5=6(9)+5=54+5=59<\/li>\n<\/ul>\n<\/li>\n\n\n\n
    • Calculate the ratio<\/strong> between consecutive terms:\n
        \n
      • The ratio between a2a_2a2\u200b and a1a_1a1\u200b is: r1=a2a1=2911\u22482.636r_1 = \\frac{a_2}{a_1} = \\frac{29}{11} \\approx 2.636r1\u200b=a1\u200ba2\u200b\u200b=1129\u200b\u22482.636<\/li>\n\n\n\n
      • The ratio between a3a_3a3\u200b and a2a_2a2\u200b is: r2=a3a2=5929\u22482.034r_2 = \\frac{a_3}{a_2} = \\frac{59}{29} \\approx 2.034r2\u200b=a2\u200ba3\u200b\u200b=2959\u200b\u22482.034<\/li>\n<\/ul>\n<\/li>\n\n\n\n
      • Comparison of ratios<\/strong>:\n
          \n
        • As shown above, the ratio between a2a_2a2\u200b and a1a_1a1\u200b is approximately 2.636, while the ratio between a3a_3a3\u200b and a2a_2a2\u200b is approximately 2.034. These ratios are not equal, which indicates that the sequence does not have a constant ratio between consecutive terms.<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n

          Conclusion:<\/h3>\n\n\n\n

          Since the ratio between consecutive terms is not constant, this sequence is not a geometric sequence. A geometric sequence requires a constant ratio between consecutive terms, and since this condition is not met, the sequence does not qualify as geometric.<\/p>\n\n\n\n

          Therefore, the correct conclusion is that the sequence is not geometric<\/strong>.<\/p>\n\n\n\n

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

          . The given sequence is not a geometric sequence. Explanation: A geometric sequence is defined by a constant ratio between consecutive terms. In this case, the sequence is defined by the formula a_n = 6n^2 + 5. To check if it’s geometric, we need to see if the ratio of consecutive terms is constant. Let’s […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-42713","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/42713","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=42713"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/42713\/revisions"}],"predecessor-version":[{"id":42715,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/42713\/revisions\/42715"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=42713"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=42713"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=42713"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}