Show that the sequence $a_n = -n+2$ is equal to $a_n = a_{n-1} + 2a_{n-2} + 2n - 9$ My Working: 
\begin{align}
a_0=&-0+2=2\\
a_1=&-1+2=1\\
a_2=&-2+2=0.
\end{align}
and $$a_2=a_{2-1}+2a_{2-2}+2(2)-9=-4.$$
I don't know what's wrong with my solution. I used this method on various questions but now I'm just ending up with the wrong answer.

Solving it further we have -
$a_{2} = a_{2-1} + 2a_{2-2} + 2(2) - 9$
$a_{2} = a_{1} + 2a_{0} + 2(2) - 9$
$a_{2}$ = 1 + 2(2) + 2(2) - 9$
$a_{2}$ = 1 + 4 + 4 - 9$
= 0
Your mistake is you are using the value of $a_{0}$ = 0 but it is 2.
