Find sequence using sum of sequence (2)

Algebra Level pending

Let \(S_n\) be the sum of a sequence \(\{a_n\}\) from \(a_1\) to \(a_n.\) If \(\{a_n\}\) is defined by \[a_1 =2 \ , a_2=5 \ , \ a_n=3S_{n+1} -S_{n+2}-2S_n,\] what is \(a_{10}?\)

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