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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 Differences for Arithmetic: Determine if the sequence is arithmetic by checking if the differences between consecutive terms are constant.Given sequence: Calculate the differences between consecutive terms: , , .The consecutive differences in the sequence are equal.
- Confirm Arithmetic Sequence: Since the consecutive differences are equal, we can conclude that the sequence is an arithmetic sequence.An arithmetic sequence is defined by having a common difference between consecutive terms.
- Check Ratios for Geometric: To confirm that the sequence is not geometric, check if the ratios between consecutive terms are constant.Calculate the ratios between consecutive terms: , , .The ratios between consecutive terms are not equal.
- Confirm Not Geometric: Since the sequence has a common difference but not a common ratio, it is not a geometric sequence.A geometric sequence is defined by having a common ratio between consecutive terms.
- Final Conclusion: Based on the previous steps, we can conclude that the sequence is an arithmetic sequence and not a geometric sequence.Therefore, the correct choice is arithmetic.
