Is the following sequence increasing strictly? If it converges, why?

Question

$$x_{n+1} = 3x_n^2+\frac{1}{12}$$ With initial starting value $x_0=0$

If it converges I can just substitute $x$ with $A$ and solve for $A$ to calculate the limit, right?

Answer 1

It will depend on the starting point.
If $x_1 > x_0$, then you can show by induction that $x_{n+1} > x_n$. But in that case it won't converge.

Answer 2

First send complete question. What is the initial value $x_0$? Put $x_{n+1}=x_n=A$.Then solve the equation. Which point is convergent point depend on the nature of the sequence. This is the method of this sort of problems.