alrite seems no one wants to answer this Q probably because it is too easy...

after read it a few more times I think I see it

so I just answer myself:

to see this: split LHS p_{k}in to 1/2(p_{k}+ p_{k}) and the first equation becomes 1/2(p_{k}+ p_{k})= 1/2 (p_{k+1}+ p_{K-1})

rewrite above in to: 1/2(p_{k+1}-p_{k}) = 1/2(p_{k}-p_{K-1}) which is: 1/2b_{k+1}= 1/2b_{k}gives us b_{k}= b_{k-1}