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What kind of sequence is this?\newline91,91,91,91,…91, 91, 91, 91, \dots\newlineChoices:\newline(A) arithmetic\newline(B) geometric\newline(C) both\newline(D) neither

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Q. What kind of sequence is this?\newline91,91,91,91,…91, 91, 91, 91, \dots\newlineChoices:\newline(A) arithmetic\newline(B) geometric\newline(C) both\newline(D) neither
  1. Verify Consecutive Differences: Let's verify if the differences between consecutive terms are uniform. Given sequence: 91,91,91,91,ext...91, 91, 91, 91, ext{...} Are the consecutive differences in the sequence equal? 91−91=091 - 91 = 0, 91−91=091 - 91 = 0, 91−91=091 - 91 = 0. The consecutive differences in the sequence are equal and are all zero.
  2. Check Equal Ratios: Let's check whether the ratios between consecutive terms are equal. Given sequence: 91,91,91,91,ext...91, 91, 91, 91, ext{...} Are the ratios between consecutive terms in the sequence equal? 91/91=191 / 91 = 1, 91/91=191 / 91 = 1, 91/91=191 / 91 = 1. Yes, the sequence has a common ratio of 11.
  3. Sequence Characteristics: Arithmetic sequence: Consecutive terms have a common difference. Geometric sequence: Consecutive terms have a common ratio. The sequence 91,91,91,91,…91, 91, 91, 91, \ldots has both a common difference of 00 and a common ratio of 11. Therefore, it is both an arithmetic and a geometric sequence.

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