# Thread: [SOLVED] simple difference equation

1. ## [SOLVED] simple difference equation

if p=q-1. and$\displaystyle h_{k}=ph_{k+1}+qh_{k-1}$ and $\displaystyle h_{1}=ph_{2}+q$ for k=1 than how by using difference equation theory is a G.S $\displaystyle h_{k}=A+B(\frac{q}{p})^k$? I can just about see where you get$\displaystyle 1^k$ but not$\displaystyle (\frac{q}{p})^k$ thanks

2. Some observations

Originally Posted by oxrigby
if p=q-1. and$\displaystyle h_{k}=ph_{k+1}+qh_{k-1}$ and $\displaystyle h_{1}=ph_{2}+q$ for k=1
$\displaystyle \implies h_0 = 1$

Originally Posted by oxrigby
$\displaystyle h_{k}=A+B(\frac{q}{p})^k$? I can just about see where you get$\displaystyle 1^k$ but not$\displaystyle (\frac{q}{p})^k$ thanks
$\displaystyle \implies 1 =A+B$

3. still makes no sense,,,why q/p?
$\displaystyle px^2-x+q=0$
$\displaystyle x(px-1)+q=0$
$\displaystyle px-1=-1+p$
implies x=1. i.e $\displaystyle h_{k}=A.1^k$ how does x =q/p?