I was given some information:

An animal population grows by 8% every year, and in addition 40 individual move there at the end of each year. At the beginning of the first year the size of the population is 2000.

Determine a recursive sequence, which gives the number of individuals in the population at the beginning of the year n.

Thus

an= 1,08*an-1+40(from the previous year)

Then the exericise asks for the general equation for the population. By deriving the equation, I get $\displaystyle 0,8*{n-1}*2000+ 250(1-0,8^{n-1})$

Yet the answer in the book states

$\displaystyle 1750*08^{n-1}+250$.

And I don't know how they get it.

Any help is hugely appreciated, since I have a test soon, and currently am barely reaching the level required to pass.

Thank you in advance!