Find limit of recursive sequence

$0 \leq a\leq \frac{1}{4}$

$a_{1} = a,$ $a_{n+1} = a + (a_{n})^{2}$

I have to prove that the sequence has a limit, and to find the limit $a_{n}$.

Actually, I have no idea what to do.
I just know that the sequence is monotonic increasing, and I dont know why, i think that the lim is $a$.
Thanks.