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What kind of sequence is this?\newline1,5,25,125,1, 5, 25, 125, \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?\newline1,5,25,125,1, 5, 25, 125, \dots\newlineChoices:\newline(A) arithmetic\newline(B) geometric\newline(C) both\newline(D) neither
  1. Given Sequence Analysis: Let's look at the given sequence: 1,5,25,125,1, 5, 25, 125, \ldots\newlineTo identify if it's an arithmetic sequence, we need to check if the difference between consecutive terms is constant.\newlineDifference between second and first term: 51=45 - 1 = 4\newlineDifference between third and second term: 255=2025 - 5 = 20\newlineSince the differences are not the same, it is not an arithmetic sequence.
  2. Arithmetic Sequence Check: Now, let's check if it's a geometric sequence by finding the ratio between consecutive terms.\newlineRatio of second to first term: 51=5\frac{5}{1} = 5\newlineRatio of third to second term: 255=5\frac{25}{5} = 5\newlineRatio of fourth to third term: 12525=5\frac{125}{25} = 5\newlineSince the ratios are the same, it is a geometric sequence.

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