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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
- Check for Arithmetic: Let's first check if the sequence is arithmetic by finding the differences between consecutive terms. Given sequence: Are the consecutive differences in the sequence equal? Let's calculate:,,.The consecutive differences in the sequence are not equal.
- Check for Geometric: Since the sequence is not arithmetic, let's check if it's geometric by finding the ratios between consecutive terms. Given sequence: Are the ratios between consecutive terms in the sequence equal? Let's calculate:,,.Yes, the sequence has a common ratio of .
- Determine Sequence Type: Now, let's determine the type of sequence based on our findings. An arithmetic sequence has a common difference between consecutive terms, while a geometric sequence has a common ratio between consecutive terms. Since we found that the sequence has a common ratio and not a common difference, it is a geometric sequence.
