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What kind of sequence is this?\newline39,59,79,99,…39, 59, 79, 99, \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?\newline39,59,79,99,…39, 59, 79, 99, \dots\newlineChoices:\newline(A) arithmetic\newline(B) geometric\newline(C) both\newline(D) neither
  1. Check Differences Consistent: Step 11: Check if the differences between consecutive terms are consistent. Calculate the differences: 59−39=2059 - 39 = 20, 79−59=2079 - 59 = 20, 99−79=2099 - 79 = 20.
  2. Identify Arithmetic Sequence: Step 22: Since the differences are consistent, it suggests an arithmetic sequence. Check if it fits the definition of an arithmetic sequence where each term increases by a fixed amount.
  3. Verify Geometric Sequence: Step 33: Verify if it could be a geometric sequence by checking the ratios of consecutive terms. Calculate the ratios: 5939≈1.51\frac{59}{39} \approx 1.51, 7959≈1.34\frac{79}{59} \approx 1.34, 9979≈1.25\frac{99}{79} \approx 1.25. The ratios are not consistent.

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