Write a recursive formula for the following explieit formula, and find the first term of the sequence. \[ a_{n}=31+41 n \] \[ \begin{array}{l} a_{1}=\square \\ a_{\mathrm{f}}=\square \end{array} \] (Bimplify your answers.)

To create a recursive formula from the given explicit formula \( a_n = 31 + 41n \), we start with the relationship between consecutive terms. First, let's compute the first term of the sequence: \[ a_1 = 31 + 41 \cdot 1 = 31 + 41 = 72 \] Now, we can express the recursive relation. The difference between consecutive terms \( a_{n} - a_{n-1} \) can be calculated as follows: \[ a_n = 31 + 41n \Rightarrow a_{n-1} = 31 + 41(n-1) = 31 + 41n - 41 = a_n - 41 \] Thus, we can formulate the recursive definition: \[ a_n = a_{n-1} + 41 \quad \text{for } n > 1 \] In summary, we have: \[ \begin{array}{l} a_{1}=72 \\ a_{n} = a_{n-1} + 41 \text{ for } n > 1 \end{array} \]