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What kind of sequence is this?\newline90,75,60,45,…90, 75, 60, 45, \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?\newline90,75,60,45,…90, 75, 60, 45, \dots\newlineChoices:\newline(A) arithmetic\newline(B) geometric\newline(C) both\newline(D) neither
  1. Check Differences Uniform: Step 11: Check if the differences between consecutive terms are uniform. Given sequence: 90,75,60,45,…90, 75, 60, 45, \ldots Calculate the differences: 75−90=−1575 - 90 = -15, 60−75=−1560 - 75 = -15, 45−60=−1545 - 60 = -15.
  2. Check Arithmetic or Geometric: Step 22: Since the differences between consecutive terms are equal, this suggests it might be an arithmetic sequence. Check if it's also geometric by calculating the ratios: 7590≈0.833\frac{75}{90} \approx 0.833, 6075=0.8\frac{60}{75} = 0.8, 4560=0.75\frac{45}{60} = 0.75. The ratios are not equal.

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