Show that the sequence $\displaystyle {a_{n}}$ is a solution of the recurrence relation $\displaystyle a_{n}=-3a_{n-1}+4a_{n-1}$ if $\displaystyle a_{n}=0$

So far, I plugged in $\displaystyle a_{n}=0$ to get $\displaystyle a_{n}=-3(0)+4(0)=0$ to show the sequence is a solution, but I think I'm missing a step. How can I figure out what $\displaystyle a_{n-1}$ and $\displaystyle a_{n-2}$ are?