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What kind of sequence is this?\newline64,81,100,121,…64, 81, 100, 121, \dots\newlineChoices:\newline(A) arithmetic\newline(B) geometric\newline(C) both\newline(D) neither

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Identify arithmetic and geometric sequencesright chevron icon

Full solution

Q. What kind of sequence is this?\newline64,81,100,121,…64, 81, 100, 121, \dots\newlineChoices:\newline(A) arithmetic\newline(B) geometric\newline(C) both\newline(D) neither
  1. Check Differences: To determine the type of sequence, we first need to check the differences between consecutive terms to see if it is an arithmetic sequence.\newlineLet's calculate the differences:\newline81−64=1781 - 64 = 17\newline100−81=19100 - 81 = 19\newline121−100=21121 - 100 = 21
  2. Calculate Differences: The differences between consecutive terms are not constant, so the sequence is not arithmetic.
  3. Not Arithmetic: Next, we check if it is a geometric sequence by finding the ratios between consecutive terms.\newlineLet's calculate the ratios:\newline8164=1.265625\frac{81}{64} = 1.265625\newline10081≈1.234567901\frac{100}{81} \approx 1.234567901\newline121100=1.21\frac{121}{100} = 1.21
  4. Check Ratios: The ratios between consecutive terms are not constant, so the sequence is not geometric.
  5. Calculate Ratios: Since the sequence is neither arithmetic (constant differences) nor geometric (constant ratios), the correct choice is (D)(D) neither.

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