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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 the common difference is .
- Identify Arithmetic Sequence: Since the sequence has a common difference, it is an arithmetic sequence. An arithmetic sequence is defined by having a constant difference between consecutive terms.
- Check for Geometric Sequence: Now, let's check if the sequence could also be geometric by finding the ratios between consecutive terms. does not equal , nor does it equal . The ratios between consecutive terms are not equal, so the sequence is not geometric.
- Final Conclusion: Based on the above steps, we can conclude that the sequence is arithmetic because it has a common difference, and it is not geometric because it does not have a common ratio.
