Solving single term recurrence relation?

Question

$a_n = -3a_{n-1}\\ a_0 = 2$

Therefore

$a_1 = -3(2) = -6\\ a_2 = -3(-6) = 18\\ a_3 = -3(18) = 54$

So... $x^n = -3^{n-1}$? If so $x^2 = -3^1$, so $x^2 + 3 = 0$, then $x = \pm (i\sqrt3)$. That doesn't seem right.