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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 Arithmetic Differences: Let's first check if the sequence is arithmetic by finding the differences between consecutive terms.Given sequence: Difference between second and first term: .Difference between third and second term: .Difference between fourth and third term: .We notice that the differences are not constant.
- Check Geometric Ratios: Now, let's check if the sequence is geometric by finding the ratios between consecutive terms.Given sequence: Ratio of second to first term: .Ratio of third to second term: .Ratio of fourth to third term: .The ratios between consecutive terms are constant, which means the sequence is geometric.
- Identify Sequence Type: Since the sequence has a constant ratio but not a constant difference, it is not arithmetic. It is geometric because each term after the first is obtained by multiplying the previous term by a constant ratio (which is in this case).
