Series and sequence

The population of a colony of insects increases in such a way that if it is N at the beginning of the week, then at the end of the week it is a+bN, where a and b are constants and 0<b<1. Starting from the beginning of the week when the population is N, write down an expression for the population at the end of 2 weeks. Show that at the end of c consecutive weeks the population is a(1-b^c/1-b)+b^cN.

When a=2000 and b=0.2, it is known that the population takes about 4 weeks to increase from N to 2N. Estimate a value for N from this information.

So how far have you got with this?
Can you show us some working?

I really don't know how to solve it...
I can't understand the question, it is A.P. or G.P.?

You have been given a formula


Start of W1 = N

End of W1 = a+bN

So start of W2 = a+bN

So what is end of W2

End of W2 = a+bN+(a+bN-N)= 2a+2bN-N
Is it correct?

I really don't know how to solve it...
I can't understand the question, it is A.P. or G.P.?

Forget about APs and GPs for the moment and just use the formula as TenOfThem suggests.

Whatever the start-value is at the beginning of the week, you are told that the end-value at the end of the week is given by the formula

end-value = a + b x start-value

So if you start the week with N, you end the week with a + bN.
So if you start the 2nd week with a + bN, what is the value at the end of the 2nd week?

a+b(a+bN)
i knew how to show it ,but now i don't know how to estimate a value for N.