Write a recursive formula for the following explicit formula, and find the first term of the sequence. \( a_{n}=31+41 \mathrm{n} \) \( a_{1}=\square \) \( a_{n}=\square \) (Simplify your answers.)

To derive a recursive formula for the given explicit formula \( a_{n}=31+41n \), we first find the first term of the sequence using \( n=1 \). Calculating \( a_{1} \): \[ a_{1} = 31 + 41(1) = 31 + 41 = 72 \] Now, for the recursive formula, the sequence can also be defined based on the previous term. Observing the difference between successive terms: \[ a_{n} - a_{n-1} = (31 + 41n) - (31 + 41(n-1)) = 41 \] Thus, the recursive formula is: \[ a_{1} = 72 \] \[ a_{n} = a_{n-1} + 41 \text{ for } n > 1 \] So, we have: \( a_{1}=72 \) \( a_{n}=a_{n-1}+41 \)