Answer
$a_n=8n+17$
Work Step by Step
We know that the general formula of an arithmetic sequence is given by
$a_n= a_1+(n-1) d$ ...(1)
For $n=9$ and $n=15$ we have $a_9=a_1+8d$ ..(2)
$a_{15}=a_1+14d$ ..(3)
Now, we have $a_{15}-a_9=(a_1+14d)-(a_1+8d) $
This gives: $137-89=6d \implies d=\dfrac{48}{6}=8$
$a_9=a_1+8d \implies a_1 =a_9-8d=89-(8)(8)=25$
From equation (1) we have $a_n=25+(n-1) 8=25+8n-8$
Thus, $a_n=8n+17$
