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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
- Find Differences: To determine the type of sequence, we need to look at the differences or ratios between consecutive terms.First, let's find the differences between consecutive terms to see if it is an arithmetic sequence.Difference between the first and second term: Difference between the second and third term: Difference between the third and fourth term:
- Check Arithmetic Sequence: Now, let's check if the differences are consistent, which would indicate an arithmetic sequence. (first difference) is not equal to (second difference), which is not equal to (third difference).Since the differences are not consistent, it is not an arithmetic sequence.
- Check Geometric Sequence: Next, let's check if there is a common ratio between terms, which would indicate a geometric sequence.Ratio between the first and second term: Ratio between the second and third term: Ratio between the third and fourth term:
- Calculate Ratios: We will calculate the ratios to see if they are consistent.First ratio: Second ratio: Third ratio: The ratios are not consistent, so it is not a geometric sequence.
- Final Conclusion: Since the sequence is neither arithmetic (because the differences are not consistent) nor geometric (because the ratios are not consistent), the correct choice is:(D) neither
