To complete the recursive formula of the arithmetic sequence 9, -1, -11, -21, we need to identify the first term and the common difference.
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First term (d(1)): The first term of the sequence is 9. Thus, \( d(1) = 9 \).
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Common difference: To find the common difference (d), we subtract the first term from the second term: \[ -1 - 9 = -10 \]
Now, let's confirm that this common difference holds for the subsequent terms:
- From -1 to -11: \[ -11 - (-1) = -10 \]
- From -11 to -21: \[ -21 - (-11) = -10 \]
The common difference is consistent and is -10.
Now we can complete the recursive formula:
- \( d(1) = 9 \)
- \( d(n) = d(n - 1) - 10 \)
Thus, the complete recursive formula is: \[ d(1) = 9 \] \[ d(n) = d(n - 1) - 10 \]