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What kind of sequence is this?\newline4,20,100,500,…4, 20, 100, 500, \ldots\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?\newline4,20,100,500,…4, 20, 100, 500, \ldots\newlineChoices:\newline(A) arithmetic\newline(B) geometric\newline(C) both\newline(D) neither
  1. Check Arithmetic Sequence: Let's check if the sequence is arithmetic by finding the difference between consecutive terms.\newlineDifference between second and first term: 20−4=1620 - 4 = 16\newlineDifference between third and second term: 100−20=80100 - 20 = 80\newlineSince the differences are not the same, the sequence is not arithmetic.
  2. Check Geometric Sequence: Now, let's check if the sequence is geometric by finding the ratio between consecutive terms.\newlineRatio of second to first term: 204=5\frac{20}{4} = 5\newlineRatio of third to second term: 10020=5\frac{100}{20} = 5\newlineSince the ratios are the same, the sequence is geometric.

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