Q:

Calculate population after time

I want to know how to calculate following
We have one female that gives birth to one child every year for 10 years. Out of
10 children 5 are female and after 20 years they can reproduce as well. How could
I calculate total population after specified time and with different starting
number.
I am not math student and I haven't had any math classes in long time, if somebody
can please show me how can I calculate things like this.
Thanks

A:

okay so the original few generations look like this:

1
10
50
250
1250

so this ( other than the original one) is $10\cdot 5^{n-1}$ in generation n ( assuming the 1 is generation 0). Now you say they last 60 years, each generation is produced in 20, that makes three generations, so what is $10\cdot 5^{n-1}+10\cdot 5^n+10\cdot 5^{n+1}$  that's 10 times the sum of the powers of 5 involved or 10 times the sum of a finite geometric series ( admittedly I can't remember the formula for solving that sum right now). at that point you can solve for the population at any time after the first 60 years. 

