How do you find a formula for the nth term of the sequence that satisfies: $x_n$$_+$$_1$=$-4x_n$-$4x_n$$_-$$_1$?
$x_0 = 1$, $x_1 = 0$
I substituted $x_n$ = $x^n$ then found that the roots of the quadratic are coincident roots, -2 repeated but I don't know what to do know.
The characteristic equation is $x^2+4x+4=0$, so it has a double root in $-2$.
Therefore, we have $x_n=a(-2)^n+bn(-2)^n$.
For $n=0$, we have $a=1$, for $n=1$, we have $0=-2a-2b$, so $b=-1$.
We have $x_n=(1-n)(-2)^n$.