# Dio-sequence (Part 1)

Algebra Level pending

A strictly increasing sequence of positive integers $$a_1$$, $$a_2$$, $$a_3$$,... 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. If $$a_{13}=2016$$, compute $$a_1$$.

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