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What kind of sequence is this?\newline174,182,187,189,…174, 182, 187, 189, \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

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Q. What kind of sequence is this?\newline174,182,187,189,…174, 182, 187, 189, \dots\newlineChoices:\newline(A) arithmetic\newline(B) geometric\newline(C) both\newline(D) neither
  1. List Sequence Pattern: Let's list the given sequence and observe the pattern.\newlineSequence: 174174, 182182, 187187, 189189, ...
  2. Check Arithmetic Differences: Check if the sequence is arithmetic by finding the differences between consecutive terms.\newline182−174=8182 - 174 = 8\newline187−182=5187 - 182 = 5\newline189−187=2189 - 187 = 2\newlineThe differences are not the same, so the sequence is not arithmetic.
  3. Check Geometric Ratios: Check if the sequence is geometric by finding the ratios between consecutive terms. \newline182174≈1.046\frac{182}{174} \approx 1.046\newline187182≈1.027\frac{187}{182} \approx 1.027\newline189187≈1.011\frac{189}{187} \approx 1.011\newlineThe ratios are not the same, so the sequence is not geometric.
  4. Sequence Classification: Since the sequence has neither a common difference nor a common ratio, it is neither arithmetic nor geometric.

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