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A strictly increeasing sequence of posit...

A strictly increeasing sequence of positive integers `a _(1), a _(2), a _(3)…` has the property that for ever positive integer `k,` the subsequence `a _(2k -1), 2 _(2k), a _(2k +1)` is geometric and the subsequence `a _(2k), 2 _(2k +1), a _( 2k +2)` is arithmetic. Suppose that `a _(13)= 2016.` Find `a _(1).`

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