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What kind of sequence is this?\newline95,190,380,760,…95, 190, 380, 760, \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?\newline95,190,380,760,…95, 190, 380, 760, \dots\newlineChoices:\newline(A) arithmetic\newline(B) geometric\newline(C) both\newline(D) neither
  1. Check Arithmetic Differences: Let's first check if the sequence is arithmetic by finding the differences between consecutive terms. Given sequence: 95,190,380,760,…95, 190, 380, 760, \ldots\newlineCalculate the differences: 190−95=95190 - 95 = 95, 380−190=190380 - 190 = 190, 760−380=380760 - 380 = 380.\newlineCheck if the differences are equal: 95,190,38095, 190, 380.\newlineThe differences are not equal, so the sequence is not arithmetic.
  2. Calculate Ratios for Geometric Sequence: Now, let's check if the sequence is geometric by finding the ratios between consecutive terms. Given sequence: 95,190,380,760,…95, 190, 380, 760, \ldots\newlineCalculate the ratios: 19095=2\frac{190}{95} = 2, 380190=2\frac{380}{190} = 2, 760380=2\frac{760}{380} = 2.\newlineCheck if the ratios are equal: 2,2,22, 2, 2.\newlineThe ratios are equal, so the sequence is geometric.

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