I'm working on a recursive function for my IB Maths exploration, of the form $f(x)=f((x+a)^{-b})$ I've worked out a general formula for the n-th term of the sequence when $b = 1$, but whenever I'm trying to apply my knowledge to $b = 2$ or higher I end up with a ton of algebra and I'm not able to derive a general formula, is there any way that I can use to express the sequence? (terms ahead) $$ y = x + a $$
$$U_1=1/y^b $$ $$U_2 = {y^{b^2}\over(ay^b+1)^b} $$ $$U_3={(ay^b+1)^{b^2}\over(y^{b^2}+(ay^b+1)^b)^b} $$ $$U_4={(y^{b^2}+(ay^b+1)^b)^{b^2}\over((ay^b+1)^{b^2}+(y^{b^2}+(ay^b+1)^b)^b)^b} $$
I'm sorry for the poor formatting of the sequence but I'm still getting started with this system.