We have a markov chain with states $\{1,2,3,4,5 \}$ with $A = \{1,5\}$ being our absorbing states. We take a step forward with probability P, and step backwards with probability Q.
Let $T_k $ be the number of steps to hit $A$ (either 1 or 5), and let $k = 1,2,3,4,5$
Using $ G_k(s) = E(s^{T_k}) $ as the probability generating function, we want to show that $$ G_3(s) = \frac{(p^2+q^2)s^2}{1-2pqs^2} $$
So, I'm kind of lost on how to start this. What is the first step to tackling a question like this?