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What kind of sequence is this?\newline115,102,89,76,…115, 102, 89, 76, \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?\newline115,102,89,76,…115, 102, 89, 76, \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: 115,102,89,76,ext...115, 102, 89, 76, ext{...} Calculate the differences: 102−115=−13102 - 115 = -13, 89−102=−1389 - 102 = -13, 76−89=−1376 - 89 = -13.
  2. Arithmetic Sequence Check: Step 22: Since the differences between consecutive terms are equal, this suggests it might be an arithmetic sequence. Check if it fits the definition of an arithmetic sequence where each term after the first is obtained by adding a constant difference to the preceding term.
  3. Geometric Sequence Verification: Step 33: Verify if the sequence could also be geometric by checking if the ratios between consecutive terms are equal. Calculate the ratios: 102115≈0.88696\frac{102}{115} \approx 0.88696, 89102≈0.87255\frac{89}{102} \approx 0.87255, 7689≈0.85393\frac{76}{89} \approx 0.85393. The ratios are not equal.

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