Question

find algebraic form (Xn) of algebraic sequence 7, -5, -3​

Answer 1

X1=21/2  and Xn+1=(2+Xn)1/2 for each n≥1.

Find the supremum of the set {Xn} and prove it.

I figured that the supremum should be 2 by just examining the elements of the set and from the fact that each element is less than 2. Is there a proper way to find and prove the supremum of this set?