I am stuck on this question, and do not know where to head with it.
Find the solution to An= 2An-1 + An-2 - 2An-3 for n=2,3,4,5......, with a0=3, a1=6 and a2=0
(Note that n-1, n-2, n-3 are subscripts)
Hi
Well it depends by your level in maths
The characteristic polynomial is $\displaystyle x^3-2x^2-x+2$ whose roots are -1, 1 and 2
$\displaystyle a_n = \alpha \-1)^n + \beta \: 1^n + \gamma \: 2^n$
$\displaystyle \alpha$, $\displaystyle \beta$, $\displaystyle \gamma$ values are found by the values of $\displaystyle a_0$, $\displaystyle a_1$, $\displaystyle a_2$
$\displaystyle a_n = -2 \-1)^n + 6 \:\: 1^n - 2^n$