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What kind of sequence is this?\newline976,976,976,976,…976, 976, 976, 976, \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?\newline976,976,976,976,…976, 976, 976, 976, \ldots\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: 976,976,976,976,ext...976, 976, 976, 976, ext{...} Are the consecutive differences in the sequence equal? 976−976=0976 - 976 = 0, 976−976=0976 - 976 = 0, 976−976=0976 - 976 = 0. The consecutive differences in the sequence are equal and are all zero.
  2. Check Equal Ratios: Now, let's check whether the ratios between consecutive terms are equal. Given sequence: 976,976,976,976,ext...976, 976, 976, 976, ext{...} Are the ratios between consecutive terms in the sequence equal? 976/976=1976 / 976 = 1, 976/976=1976 / 976 = 1, 976/976=1976 / 976 = 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 976,976,976,976,…976, 976, 976, 976, \ldots 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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