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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
- Identify 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 the terms.Difference between the first and second term: Difference between the second and third term: Difference between the third and fourth term:
- Check for Arithmetic Sequence: Now, let's check if the differences are constant, which would indicate an arithmetic sequence.Difference between the first and second term: Difference between the second and third term: Difference between the third and fourth term: The differences are not constant; they are decreasing by each time (, , ).This means the sequence is not arithmetic.
- Check for Geometric Sequence: Next, let's check if there is a common ratio, which would indicate a geometric sequence.To do this, we divide each term by the previous term.Second term / First term: Third term / Second term: Fourth term / Third term: We need to calculate these ratios to see if they are the same.
- Calculate Ratios: Let's calculate the ratios:Second term / First term: Third term / Second term: Fourth term / Third term: The ratios are not constant; they are different for each pair of terms.This means the sequence is not geometric.
- Final Conclusion: Since the sequence is neither arithmetic (the differences are not constant) nor geometric (the ratios are not constant), the correct choice is:(D) neither
