Checking recurrence relation

Question

Is there a way to check my recurrence relation, so I can confirm I did it correctly?

$a_k = -4a_{k-1} -4a_{k-2}$ with $a_0 = 0$ $a_1= -1$

My answer: $a_n = 0(-2)^n - ½n(-2)^n$

Answer 1

Yes, there is a way to check your result. Calculate $a_0,a_1,a_2,a_3,a_4\dots$ using the recurrence relation $a_k=-4a_{k-1}-4a_{k-2}$, and also calculate them using your formula $a_n=-\frac12(-2)^n$, and see if you get the same numbers.