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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 Uniform: Let's verify if the differences between consecutive terms are uniform. Given sequence: Are the consecutive differences in the sequence equal? Let's calculate the differences: , , . The consecutive differences in the sequence are equal.
- 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. In this case, the common difference is .
- Check for Geometric Sequence: Now, let's check whether the sequence could also be geometric by finding the ratios between consecutive terms. Given sequence: Are the ratios between consecutive terms in the sequence equal? Let's calculate the ratios: , , . The ratios between consecutive terms are not equal.
- Sequence Analysis 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, which is not the case here.
