Using induction to prove a formula

Question

Suppose $~a_0 = 1~$ and $~a_n = 2a_{n−1} + 3~$ for all $~n ≥ 1$. Using proof by induction, prove that the formula for an for all $~n ≥ 0~$ is given by $~a_n = 2^{n+2} − 3$.

How can I solve this question?

Answer 1

Hint: $a _ n + 3 = 2 ( a_{n-1} +3) $.