Question 10
A strictly increasing sequence of positive integers $a_1,$ $a_2,$ $a_3,$ $\ldots$ has the property that for every positive integer $k,$ the subsequence $a_{2k-1},$ $a_{2k},$ $a_{2k+1}$ is geometric and the subsequence $a_{2k},$ $a_{2k+1},$ $a_{2k+2}$ is arithmetic. Suppose that $a_{13} = 2016.$ Find $a_1.$