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What kind of sequence is this?\newline2,4,8,16,…2, 4, 8, 16, \ldots\newlineChoices:\newline(A) arithmetic\newline(B) geometric\newline(C) both\newline(D) neither

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Full solution

Q. What kind of sequence is this?\newline2,4,8,16,…2, 4, 8, 16, \ldots\newlineChoices:\newline(A) arithmetic\newline(B) geometric\newline(C) both\newline(D) neither
  1. Check Differences Uniform: Step 11: Check if the differences between consecutive terms are uniform. Given sequence: 2,4,8,16,…2, 4, 8, 16, \ldots Calculate the differences: 4−2=24 - 2 = 2, 8−4=48 - 4 = 4, 16−8=816 - 8 = 8.
  2. Check Ratios Consistent: Step 22: Check if the ratios between consecutive terms are consistent. Given sequence: 2,4,8,16,…2, 4, 8, 16, \ldots Calculate the ratios: 42=2\frac{4}{2} = 2, 84=2\frac{8}{4} = 2, 168=2\frac{16}{8} = 2.
  3. Determine Sequence Type: Step 33: Determine the type of sequence. Since the differences are not the same 2,4,82, 4, 8, it's not arithmetic. The ratios are the same 2,2,22, 2, 2, indicating it's a geometric sequence.

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