Monotonicity of a recursively defined sequence $s_{n+1} = \sqrt{4s_n -1}$

Question

I am trying to answer this question:

Let $s_1 = k$ and $s_{n+1} = \sqrt{4s_n -1}$. For what values of $k$ will the sequence $s_n$ be monotone increasing?

I know the definition of monotone increasing , it's that $s_n \le s_{n+1}$ for all $n$.

But how can i prove something like that , i just need some hints?

Thanks.