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?