I have trouble with following question and I was wondering if someone can help me.

Forrecurrence relation an = 2an-1 +an-2, a1 = 5 and a2 = 10. Use mathematical induction to show that an < 3^nfor all n >3.

This is how I tried.

Basic step p(3) = 2(10) + 5 = 25 < 3^3

So p(3) is true

Inductive step

an < 3^n

2an + ak-1 < 2*3^n + ak-1

ak+1 < 2*3^n + ak-1

I would appreciate any help.

Thanks