TITLE: Convergent Sequence Terminology
QUESTION [5 upvotes]: What is the following sequence classified as?  I don't want to make anybody solve it, I just need to know where to begin looking to solve it.
$$\alpha_1 = \sqrt{20}$$
$$\alpha_{n+1} = \sqrt{20 + \alpha_n}$$
I am suppose to prove that it converges to 5, however if I could just get a little terminology help it is more then appreciated!
Note: I updated the terminology, as well as give the initial value.
Thanks!

REPLY [2 votes]: In addition to the excellent hinting of Arturo, I say that it might be useful to consider the intuitively-inappropriate statement that $ x = \sqrt{20 + x} $, or rather that $x^2 = 20 + x$.
To be clear, the existence of a solution to this statement does not imply the existence of a solution to your recurrence, but after following Arturo's hints...
Good luck!