Given recurrence relation is : $A_n=17A_{n-1}+30n\ldots\ldots (i)$
Using the same relation we can write $A_{n-1}=17A_{n-2}+30(n-1)$
Putting the value of $A_{n-1}$ is $(i)$
$A_n=17^2A_{n-2}+30[n+17(n-1)]$
Repeat this process until you get $A_0$ in the equation.