Školjka

%V0 A sequence of real numbers $u_1, u_2, u_3, \dots$ is determined by $u_1$ and the following recurrence relation for $n \geq 1$: $$4u_{n+1} = \sqrt[3]{ 64u_n + 15.}$$ Describe, with proof, the behavior of $u_n$ as $n \to \infty.$