Question 3Suppose that a given sequence $\{x_n\}$ satisfies the conditions that $x_1=1$ and, for $n\ge1$, $$x_{n+1}=\frac1{16}\left(1+4x_n+\sqrt{1+24x_n}\right).$$ Determine $\displaystyle\lim_{n\to\infty}3x_n$.