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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?

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    @liangneh: The correction of the first typo should have been to $a_n=c\cdot a_{n-1}$. The correction you made is correct, but not as helpful. The next typo, on the third displayed line, remains uncorrected as of now.2011-05-05

1 Answers 1

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Even if that first equation is a typo, that is the correct general solution. If a proof is necessary, I suggest using Induction on $n$.

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    this is not a proving question2011-05-05