To complete the recursive formula for the given arithmetic sequence \(4, 22, 40, 58, \ldots\), we need to find the first term and the common difference.
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First Term (b(1)): The first term \(b(1)\) is the first term of the sequence, which is 4. \[ b(1) = 4 \]
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Common Difference: To find the common difference \(d\), we can subtract the first term from the second term: \[ d = 22 - 4 = 18 \] The common difference can also be verified with the other terms: \[ 40 - 22 = 18 \quad \text{and} \quad 58 - 40 = 18 \] So, the common difference \(d = 18\).
Putting it all together, we can write the recursive formula as follows: \[ b(n) = b(n - 1) + 18 \]
Thus, the completed recursive formula is: \[ b(1) = 4 \] \[ b(n) = b(n - 1) + 18 \]