Suppose a parent has no offspring with $p=\frac{1}{4}$ and two offspring with $p=\frac{3}{4}$. Obtain a recursion equation for $u_n$.

Question

Suppose a parent has no offspring with $p=\frac{1}{4}$ and two offspring with $p=\frac{3}{4}$. Obtain a recursion equation for $u_n$, the probability that the population is extinct by $n$.

I've been able to do the first part of the question i.e. finding the recursion equation for $u_{n}$ .

i.e. $u_{n+1} = \frac{1}{4} + \frac{3}{4} u_{n}^2$.

How do I find the probability that the population is extinct by $n$? Do I use extinction probability i.e. $P ( N \leq n)$ ?

Thanks