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What kind of sequence is this?\newline123,123,123,123,…123, 123, 123, 123, \ldots\newlineChoices:\newline(A) arithmetic\newline(B) geometric\newline(C) both\newline(D) neither

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Q. What kind of sequence is this?\newline123,123,123,123,…123, 123, 123, 123, \ldots\newlineChoices:\newline(A) arithmetic\newline(B) geometric\newline(C) both\newline(D) neither
  1. Verify Differences Uniform: Let's verify if the differences between consecutive terms are uniform. Given sequence: 123,123,123,123,…123, 123, 123, 123, \ldots Are the consecutive differences in the sequence equal? 123−123=0123 - 123 = 0, 123−123=0123 - 123 = 0, 123−123=0123 - 123 = 0. The consecutive differences in the sequence are equal and are all zero.
  2. Check Ratios Defined: Let's check whether the ratios between consecutive terms are defined and equal. Given sequence: 123,123,123,123,ext...123, 123, 123, 123, ext{...} Are the ratios between consecutive terms in the sequence equal? Since all terms are the same, the ratio of any term to the previous term is 123/123=1123 / 123 = 1. Yes, the sequence has a common ratio of 11.
  3. Sequence Classification: Arithmetic sequence: Consecutive terms have a common difference. Geometric sequence: Consecutive terms have a common ratio. The sequence 123,123,123,123,...123, 123, 123, 123, ... has both a common difference of 00 and a common ratio of 11. Therefore, it qualifies as both an arithmetic and a geometric sequence.

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