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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 Arithmetic Sequence: Let's first check if the sequence is arithmetic by finding the differences between consecutive terms.Difference between second and first term: .Difference between third and second term: .Difference between fourth and third term: .
- Calculate Differences: The differences between consecutive terms are not constant , so the sequence is not arithmetic.
- Check Geometric Sequence: Now, let's check if the sequence is geometric by finding the ratios between consecutive terms.Ratio of second to first term: .Ratio of third to second term: .Ratio of fourth to third term: .
- Calculate Ratios: We need to calculate the ratios to see if they are equal. (rounded to four decimal places). (rounded to four decimal places). (rounded to four decimal places).
- Neither Arithmetic nor Geometric: The ratios between consecutive terms are not equal (approximately , , ), so the sequence is not geometric.
- Neither Arithmetic nor Geometric: The ratios between consecutive terms are not equal (approximately , , ), so the sequence is not geometric.Since the sequence is neither arithmetic (no common difference) nor geometric (no common ratio), the correct choice is neither.
