Looking For An Equation

[kbrune]

Hi,

I have a scenario that I need an answer to. What I'm looking for is an equation that I can use to give me the answer to a question that
I would be able to change a few of the variables if I needed to.

The scenario:

One student starts a club. Well say a cubing club! He challenges himself to find one person per month to join the club for 12 months.
To grow the club to a larger number of people, he tells each person that he has found that they must find 1 person every 4 months to also join the club.

So what I would like to know is how to calculate, how many people are in the club after 12 months, and after 24 months. I'm hoping to get an equation that would enable me to change the frequency in which the organizer finds new recruits, the frequency in which the recruits find new people, and the amount of people in the club after a certain number of months.

Please forgive me if any of this seems off or if I have posted this in the wrong category. I haven't done any formal math since highschool and I am now 33 yrs old!!

Thank you to anyone who can help!

 

[kbrune]

Clarification (using an example):
Student A starts the club beginning 2013: end of Jan, recruits B;
end of May, B recruits C: does C now also recruit every 4 months?
Or is it only A's recruits that recruit every 4 months?

In above example, B is expected to recruit twice in 2013: by end May and by end Sep: correct?

Yes, this is very close to what I had in mind.

C in your example does follow the same rules. Every new recruit must recruit every 4 months. Only A recruits every month.
The only difference is that I would like to use the 1st of the month for any given recruit.

For example. A starts the club Jan 01 13 and recruits B on that same day. B recruits every 4 months, including the month he joined.
So, B would recruit C on April 01, D on Aug 01, and E on Dec 01.
C would recruit F on July 01 and G on Nov 01.
D would recruit H on Nov 01.
F would recruit I on Oct 01.
Then the whole process repeats itself for A's new recruit on Feb 01

I hope that makes sense. Any other clarifications?