elementary number theory - Prove that $7^n+2$ is divisible by $3$ for all $n ∈ mathbb{N}$

Use mathematical induction to prove that $7^{n} +2$
is divisible by $3$ for all $n ∈ \mathbb{N}$.

I've tried to do it as follow.

If $n = 1$ then $9/3 = 3$.
Assume it is true when $n = p$. Therefore $7^{p} +2= 3k$ where $k ∈ \mathbb{N}$. Consider now $n=p+1$. Then

$$\begin{align} &7^{p+1} +2=\\ &7^p\cdot7+ 2=\\ \end{align}$$
I reached a dead end from here. If someone could help me in the direction of the next step it would be really helpful. Thanks in advance.

Answer

Hint

If $7^n+2=3k$ then

$$7^{n+1}+2=7(\color{red}{7^n})+2=7(\color{red}{3k-2})+2.$$