Convergent Sequence Terminology 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!
 A: 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!
A: First, it's not a series, it's a sequence.  Fixed in the original.
Second, it's  a recursively defined sequence. 
A sequence is "recursively defined" if you specify some specific values and then you explain how to get the "next value" from the previous one; much like induction. Here, you are saying how to get the "next term", $\alpha_{n+1}$, if you already know the value of the $n$th term, $\alpha_n$. 
Once you know the first value, then the sequence is completely determined by that first value and the "recurrence rule" $\alpha_{n+1}=\sqrt{20+\alpha_n}$. 
Now some hints:


*

*Show the sequence is increasing.

*Show the sequence is bounded.

*Conclude the sequence converges.

*Once you know it converges, take limits on both sides of the recursion to try to figure out what it converges to.

