How to find the closed form formula of this sequence

Question

How do I find the closed form formula of the below?

$a_0 = −1$

$a_i = −5a_{i−1}$

Answer 1

I think it should read $a_i=-5a_{i-1}.$

If yes, then we have: $a_0--5^0, a_1=-5a_0=5, a_2=-5a_2=-25=-5^2, ...$

Now show by induction that

$$a_i=(-1)^{i+1}5^i.$$