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What kind of sequence is this?\newline253,240,230,223,…253, 240, 230, 223, \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?\newline253,240,230,223,…253, 240, 230, 223, \dots\newlineChoices:\newline(A) arithmetic\newline(B) geometric\newline(C) both\newline(D) neither
  1. Verify Consecutive Differences: Let's verify if the differences between consecutive terms are uniform. Given sequence: 253,240,230,223,…253, 240, 230, 223, \ldots\newlineAre the consecutive differences in the sequence equal? \newline240−253=−13240 - 253 = -13, \newline230−240=−10230 - 240 = -10, \newline223−230=−7223 - 230 = -7.\newlineThe consecutive differences in the sequence are not equal.
  2. Check Equal Ratios: Let's check whether the ratios between consecutive terms are equal. Given sequence: 253,240,230,223,…253, 240, 230, 223, \dots\newlineAre the ratios between consecutive terms in the sequence equal? \newline240253≈0.9494\frac{240}{253} \approx 0.9494, \newline230240≈0.9583\frac{230}{240} \approx 0.9583, \newline223230≈0.9696\frac{223}{230} \approx 0.9696.\newlineThe sequence does not have a common ratio.
  3. Sequence Type: Arithmetic sequence: Consecutive terms have a common difference. Geometric sequence: Consecutive terms have a common ratio. \newline253,240,230,223,…253, 240, 230, 223, \ldots What type of sequence is this? \newlineThe sequence has neither a common difference nor a common ratio. It's neither an arithmetic sequence nor a geometric sequence.

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