I have the following sequence \(\displaystyle (x_{n})_{n\geq 1}\) ; \(\displaystyle x_{n+1}=x_{n}^2-x_{n}+1\)
If \(\displaystyle x_{100}=1\) then \(\displaystyle x_{2}=?\)

I did it.I got the response 1.
In the second exercise I need to find \(\displaystyle x_{1}\) such that \(\displaystyle (x_{n})_{n\geq 1}\) is convergent.

I have the following sequence \(\displaystyle (x_{n})_{n\geq 1}\) ; \(\displaystyle x_{n+1}=x_{n}^2-x_{n}+1\)
If \(\displaystyle x_{100}=1\) then \(\displaystyle x_{2}=?\)