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What kind of sequence is this?Choices:(A) arithmetic(B) geometric(C) both(D) neither
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Q. What kind of sequence is this?Choices:(A) arithmetic(B) geometric(C) both(D) neither
- Verify Consecutive Differences: Let's verify if the differences between consecutive terms are uniform. Given sequence: Are the consecutive differences in the sequence equal? , , . The consecutive differences in the sequence are equal and are all zero.
- Check Equal Ratios: Let's check whether the ratios between consecutive terms are defined and equal. Given sequence: Are the ratios between consecutive terms in the sequence equal? Since all terms are the same, the ratio of any term to the previous term is . The sequence has a common ratio of .
- Sequence Classification: Arithmetic sequence: Consecutive terms have a common difference. Geometric sequence: Consecutive terms have a common ratio. The sequence has both a common difference of and a common ratio of . Therefore, it can be considered both an arithmetic sequence (since the difference is constant) and a geometric sequence (since the ratio is constant).
