Simple question about recursive sequence format regarding $a(n+2) = -4a(n+1) + 5a(n)$

Question

Suppose there's a recursive sequence $a(n+2) = -4a(n+1) + 5a(n)$

How can i convert it into the form $a(n)$ because I am most comfortable solving questions in this form.

I tried to find out but I'm not sure if i am correct.

To make it $a(n)$:

$\Rightarrow $ $a(n+2-2) = -4a(n+1-2) + 5a(n-2)$

$\Rightarrow $ $a(n) = -4a(n-1) + 5a(n-2)$ for $n\geq 2$

Would this be correct?

Answer 1

Yes, that works, provided that $n$ doesn't have some specific value. It works because you implicitly say "this is true for any $n$ you care to name;" that means you can swap in anything for $n$, including $n-2$, and it still works (GEdgar's comment basically shows how swapping $n-2$ in for $n$ gives you your last expression).