Recurring Theme, Part \(n+1\)

Algebra Level 5

If \(a_1=10, a_2=6\) and \(5a_{n+2}=6a_{n+1}-5a_n\) for \(n>0\), find the maximal value of \(a_n\), for all positive integers \(n\).

If you come to the conclusion that no such maximum exists, enter 666.

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