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What kind of sequence is this?\newline167,151,135,119,…167, 151, 135, 119, \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?\newline167,151,135,119,…167, 151, 135, 119, \dots \newlineChoices:\newline(A) arithmetic\newline(B) geometric\newline(C) both\newline(D) neither
  1. Identify Sequence Type: To determine the type of sequence, we need to look at the pattern of the differences or ratios between the terms.\newlineFirst, let's find the difference between the consecutive terms.\newlineDifference between the first and second term: 151−167=−16151 - 167 = -16
  2. Find Consecutive Term Differences: Now, let's check the difference between the second and third term: 135−151=−16135 - 151 = -16
  3. Check for Constant Difference: Next, we check the difference between the third and fourth term: 119−135=−16119 - 135 = -16
  4. Confirm Arithmetic Sequence: Since the difference between each pair of consecutive terms is the same (−16-16), this indicates that the sequence is an arithmetic sequence.
  5. Define Arithmetic Sequence: An arithmetic sequence is defined by a constant difference between its terms. Since we have a constant difference of −16-16, we can conclude that the sequence is arithmetic.
  6. Conclusion: Therefore, the correct choice is (A) arithmetic.

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