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What kind of sequence is this?\newline43,55,67,79,…43, 55, 67, 79, \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?\newline43,55,67,79,…43, 55, 67, 79, \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: 43,55,67,79,…43, 55, 67, 79, \ldots\newlineAre the consecutive differences in the sequence equal? \newline55−43=1255 - 43 = 12, 67−55=1267 - 55 = 12, 79−67=1279 - 67 = 12.\newlineThe consecutive differences in the sequence are equal.
  2. Identify Arithmetic Sequence: Since the consecutive differences are equal, this indicates that the sequence is an arithmetic sequence. An arithmetic sequence is defined by having a common difference between consecutive terms.
  3. Check for Geometric Sequence: Now, let's check if the sequence could also be geometric by finding the ratios between consecutive terms. 5543≈1.279\frac{55}{43} \approx 1.279, 6755≈1.218\frac{67}{55} \approx 1.218, 7967≈1.179\frac{79}{67} \approx 1.179. The ratios between consecutive terms are not equal.
  4. Conclusion: Since the sequence does not have a common ratio, it is not a geometric sequence. A geometric sequence is defined by having a common ratio between consecutive terms.

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