2016 AIME I #10

A strictly increasing sequence of positive integers a_1, a_2, a_3, \dots 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.

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