Math Help - [SOLVED] simple difference equation

1. [SOLVED] simple difference equation

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

2. Some observations

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

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

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