Answer
$d=6$.
$a_1= -53$,
$a_n=a_{n-1}+6$.
$a_n= 6n-59$
Work Step by Step
1. Based on the given conditions, we have $a_9=a_1+8d=-5$ and $a_{15}=a_1+14d=31$, thus $6d=36$ and $d=6$.
2. We can find the first term $a_1=-5-8(6)=-53$, and a recursive formula $a_n=a_{n-1}+d=a_{n-1}+6$.
3. We can find a formula for the nth term $a_n=a_1+(n-1)d=--53+(n-1)6=6n-59$
