Find the limiting value of this sequence Let $x_1=-\sqrt3$ and $x_n=-\sqrt{3-x_{n-1}} $ Evaluate $lim_{n \to \infty}x_n $. How do I do these kind of problems? A kick-off would be highly appreciated.

Hint:

let $\lim_{n\rightarrow \infty}x_n=l$

Then from your equation $$ l=-\sqrt{3-l} $$

hence $l^2=3-l$

solving we get

$$ l=\frac{-1\pm \sqrt{13}}{2} $$

I have a feeling, you should go for $l=\frac{-1- \sqrt{13}}{2} $

as every term of sequence is negative.

Where did I use the initial condition?

I dont know, if it is even required.