Pretty Simple Probability Question

[ChemIsHard]

The question is:

A couple is trying to get a child. Their probability of conception in any given monthly cycle
is 1/8
(a) What is the mean number of cycles until conception occurs (the count includes the cycle
in which conception occurs)? Neglect menopause and limited lifetime of the couple.
(b) What is the smallest n such that the probability that it takes them more than n cycles
is less than 1/2 ?

I attempted to use a binomial distribution but realized that took me no where...I know it should be somewhere within 3-5 months but I can't prove it.

I know this is simple, and that I'm likely over thinking.

Thanks in advance.

 

[CompuChip]

It sounds like a binomial distribution to me.

Anyway, can you calculate what the probability P(n) is that conception takes place in the n^th month? Because then you can simply calculate the expectation value of n through
$$E = \sum_{n = 0}^\infty n P(n)$$