Let $a_1 = 3, a_2 = 18$, and $a_n = 6a_{n-1} − 9a_{n-2}$ for each integer $n \ge 3$. Prove by strong induction that $3^n$ divides $a_n$ for all integers $n \ge 1$
I've done the base step and ih however I am stuck on the Inductive Step. I'm thinking it's something like $a_{k+1} = 6a_k - 9a_{k-1}$ but I don't know how to follow that.
Thanks in advance for the help with the Inductive Step.