For the recurrence relation:
$f_n = 2a_{n-1} - 2a_{n-2}$ I got the characteristic equation that had complex roots:
$x^2 - 2x + 2 = 0$ that gave roots $i, -i$ and I wasn't sure how to continue the solving the recurrence relation with the complex roots.
Another problem I found was with the recurrence relation:
$a_n = 4a_{n-1} - 4a_{n-2}$
I got the characteristic equation that had only 1 root:
$x^2 - 4x + 4 = 0$
$r_1$ = 2
And I wasn't sure what form to use for the general solution as it's typically of the form $a_n = c_1 * (r_1)^n + c_2 * (r_2)^n $