Maths sequence

an - 6an-1 + 8an-2 + 3 = 0
Consider an - 6an-1 + 8an-2 = 0
Its characteristic equation is x^2-6x+8=0
(x-4)(x-2)=0
x=4 or x=2
So the general solution is A4^t+B2^t
The particular solution of an - 6an-1 + 8an-2 + 3 = 0 is
C=-3/(1-6+8)=-1
So the general solution of an - 6an-1 + 8an-2 + 3 = 0 is
an=A4^t+B2^t-1
Substitute a1=1 and a2=11, we find that
A+B=2
16A+4B=12
A=1/3,B=5/3
i.e. an=(1/3)4^t+(5/3)2^t-1

2009-02-15 02:57:32 補充：
代an=an-1=an-2=C