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What kind of sequence is this?\newline208,192,179,169,…208, 192, 179, 169, \dots\newlineChoices:\newline(A) arithmetic\newline(B) geometric\newline(C) both\newline(D) neither

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Full solution

Q. What kind of sequence is this?\newline208,192,179,169,…208, 192, 179, 169, \dots\newlineChoices:\newline(A) arithmetic\newline(B) geometric\newline(C) both\newline(D) neither
  1. Check Differences: Check if the differences between consecutive terms are constant. Calculate the differences: 192−208=−16192 - 208 = -16, 179−192=−13179 - 192 = -13, 169−179=−10169 - 179 = -10.
  2. Not Arithmetic: Since the differences are not constant (−16-16, −13-13, −10-10), it's not an arithmetic sequence.
  3. Check Ratios: Check if the ratios between consecutive terms are constant. Calculate the ratios: 192208≈0.9231\frac{192}{208} \approx 0.9231, 179192≈0.9323\frac{179}{192} \approx 0.9323, 169179≈0.9441\frac{169}{179} \approx 0.9441.
  4. Not Geometric: Since the ratios are not constant 0.9231,0.9323,0.94410.9231, 0.9323, 0.9441, it's not a geometric sequence.

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