Problem

Suppose that $\{a_n\}_{n=1}^{\infty}$ is a sequence such that $a_1=5$ and $a_{n+1}=\sqrt{12+a_n}$ for $n\ge 1$. Which of the following statements is true?

(a) $-\infty<\lim_{n\to\infty}a_n\le 1$.

(b) $1<\lim_{n\to\infty}a_n\le 2$.

(c) $2<\lim_{n\to\infty}a_n\le 3$.

(d) $\lim_{n\to\infty}a_n$ does not exist.

(e) None of the above statements is true.