Geometric Distribution S1

I have this question which I'm finding hard to solve:
Each of a large number of researchers, in different parts of the country, carries out a survey in which they question randomly chosen people in turn, until they find one who admits to smoking more than 20 cigarettes a day. As soon as each researcher hasn't found one such person, the total number of people is noted. In collating the results of the survey, it is found that on average 95% of the researchers had to ask at least 30 people. Use this figure to estimate the probability that one person at random would admit more than 20 cigarettes a day.

What I think I have to do:
95/100 is the probability of success, 30 is the number of trials. I should do 95/100^30*5/100, to get the probability which is just the probability for one trial.
I don't get the right answer. The right answer is 0.0018.

Thanks in advance...

95% of researchers had to ask at least 30 people, means 5% of researchers found someone who smoked 20 or more within the first 29 people.


If we let p be the probability that a person smokes 20 or more, then

$0.05 = p +(1-p)p + ... + (1-p)^{28}p$

And solve for p. Hope you're familiar with GP.s

Edit:

Alternatively you can go with the 95% had to ask 30 or more, in which case we have:

$0.95 = (1-p)^{29}p+ (1-p)^{30}p +....$

Thanks but I don't know to do the summation of this, I know it can be factorised to p(1+(1-p)...=1, but then p=1 and I don't know what to do next