Difference equation (economic growth model)

I need to solve for the procentual growth in A in terms of the parameters. This should according to my textbook equal

I guess it IS NOT a constant but CONVERGES to the previous constant. The only thing is, I can't solve it, work it out properly...

Can anybody solve this for me or put me in the right direction ?

I hope this was placed in the right subforum. Difference equations aren't differential equations, but I don't know in what subfield of Math difference equations would fit. (I'm no math student)

This might also be pre university level math, I don't know. I have never studied difference equations in high school and took a fairly math intensive curriculum.

Many thanks in advance!