$$x_{n+1} = \frac{-50 -2\lambda+32x_n+40x^2_n+8x^3_n+\lambda^2(1+10x_n)-2\lambda(-15+18x_n+8x^2_n)}{62+8\lambda^2+44x_n+8x^2_n-4\lambda(11+4x_n)} $$
Let $\lambda = -\sqrt \frac{9}{5} $ and $ x_0 = -4.$ Determine the following limits:
$\lim \limits_{n \to \infty} \frac{\lvert\lambda-x_{2n}-\frac{5}{2}\rvert}{x_{2n}-\lambda-\frac{5}{2}}$ and $\lim \limits_{n \to \infty} \frac{\lvert\lambda-x_{2n+1}-\frac{5}{2}\rvert}{x_{2n+1}-\lambda-\frac{5}{2}}$
Not sure where to start. I've tried just plugging the values into the top formula and get some horrendous numbers which make me think its not the correct way to do it.
Thanks in advance.