Think I might need to refresh myself in power series before doing this one. Anyway, how should I proceed with this question?

Consider the Branching Process { X_n, n = 0, 1, 2, 3, ...} where X_n is the population size of the nth generation. Assume P(X_o = 1) = 1 and that the pgf of the common offspring distribution N is

A(z) = \frac{1}{3 - 2z}

(i) Express A(z) as a power series and hence find P(N=6).
(ii) If q_n = P(X_n = 0) for n = 0,1, ..., write down an equation relating q_{n+1} and q_n. Hence, or otherwise, evaluate q_n for n = 0,1,2.
(iii) Find the extinction probability q = lim_{n \rightarrow \infty} q_n.

Thank youu!