HK-PC 2017 Problem 6

Given infinite sequences $a_1,a_2,a_3,\cdots$ and $b_1,b_2,b_3,\cdots$ of real numbers satisfying $a_{n+1}+b_{n+1}=\frac{a_n+b_n}{2}$ and $a_{n+1}b_{n+1}=\sqrt{a_nb_n}$ for all $n\geq1$ . Suppose $b_{2016}=1$ and $a_1>0$ . Find all possible values of $a_1$