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What kind of sequence is this?\newline92,92,92,92,…92, 92, 92, 92, \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?\newline92,92,92,92,…92, 92, 92, 92, \dots\newlineChoices:\newline(A) arithmetic\newline(B) geometric\newline(C) both\newline(D) neither
  1. Check Arithmetic Sequence: Let's first check if the sequence is an arithmetic sequence. An arithmetic sequence is one where the difference between consecutive terms is constant.\newlineCalculation: 92−92=092 - 92 = 0, 92−92=092 - 92 = 0, 92−92=092 - 92 = 0.\newlineSince the difference between each pair of consecutive terms is 00, which is constant, the sequence is an arithmetic sequence.
  2. Check Geometric Sequence: Now, let's check if the sequence is a geometric sequence. A geometric sequence is one where the ratio between consecutive terms is constant.\newlineCalculation: 9292=1\frac{92}{92} = 1, 9292=1\frac{92}{92} = 1, 9292=1\frac{92}{92} = 1.\newlineSince the ratio between each pair of consecutive terms is 11, which is constant, the sequence is a geometric sequence.
  3. Conclusion: Since the sequence satisfies the conditions for both an arithmetic sequence (constant difference) and a geometric sequence (constant ratio), we can conclude that the sequence is both an arithmetic and a geometric sequence.

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