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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
- Arithmetic Sequence Check: An arithmetic sequence is a sequence of numbers in which each term after the first is obtained by adding a constant difference to the previous term. To determine if this is an arithmetic sequence, we need to check if the difference between consecutive terms is constant.Calculation:
- Geometric Sequence Check: A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a constant ratio. To determine if this is a geometric sequence, we need to check if the ratio between consecutive terms is constant.Calculation:
- Arithmetic Sequence Result: Since the difference between consecutive terms is , it satisfies the condition for an arithmetic sequence where the common difference is .
- Geometric Sequence Result: Since the ratio between consecutive terms is , it satisfies the condition for a geometric sequence where the common ratio is .
- Overall Sequence Classification: Therefore, the sequence is both an arithmetic sequence with a common difference of and a geometric sequence with a common ratio of .
