With a given example
$$ a_{n-1} = ca_{n-2} $$
general solution:
$$ a_{n} = c . c . a_{n-2} $$
$$ = c . c . a_{n-3} $$
$$ = c^n a_0 $$
Question: Find the general solution for the homogeneous equation $$ a_{n} = 5a_{n-1} $$
General solution:
$$ a_{n} = 5^n a_{0} $$
Is my general solution correct based on the given example?