To find the recursive formula for the arithmetic sequence −6, 1, 8, 15,..., we first determine the first term and the common difference.
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The first term \( a_1 = -6 \).
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The common difference can be found by subtracting the first term from the second term: \[ d = 1 - (-6) = 1 + 6 = 7. \]
Thus, the common difference \( d = 7 \).
Now we can write the recursive formula:
- The first term: \( a_1 = -6 \).
- The recursive step: \( a_n = a_{n-1} + 7 \) for \( n > 1 \).
So the recursive formula is: \[ \begin{align*} a_1 &= -6, \ a_n &= a_{n-1} + 7 \quad \text{for } n > 1. \end{align*} \]
However, it appears that none of the given response options match the values found above. Please ensure any options given correctly reflect the initial term \( -6 \) and the proper common difference of \( 7 \).