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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
- Observation of Sequence: The given sequence is We can observe that each term is obtained by multiplying the previous term by .
- Confirmation of Arithmetic Sequence: To confirm if the sequence is arithmetic, we check if the difference between consecutive terms is constant.The difference between the second term () and the first term () is .The difference between the third term () and the second term () is .Since the differences are not constant, the sequence is not arithmetic.
- Confirmation of Geometric Sequence: To confirm if the sequence is geometric, we check if the ratio between consecutive terms is constant.The ratio of the second term () to the first term () is .The ratio of the third term () to the second term () is .Since the ratios are constant, the sequence is geometric.
- Conclusion: Based on the constant ratio between consecutive terms, we can conclude that the sequence is a geometric sequence.
