Question 3The positive real sequence $(x_n)$ is defined by $$x_1=1,\quad x_2=9,\quad x_3=9,\quad x_4=1,\qquad x_{n+4}=\sqrt[4]{x_nx_{n+1}x_{n+2}x_{n+3}}\quad(n\ge1).$$ Prove that it has a limit and find the limit.