Andrew's recursive dream

Once Andrew was trying hard to sleep (slack people motivated him to) and finally he was asleep. However during his sleep he thought upon the recursive relations which was a topic of the problem writing party. In his dream , he came across a certain sequence \(a_1,a_2,a_3 \dots ,a_{n+1}\) which followed the recurrence relation \(a_{k+1}=2a_{k-1}+3a_k\) for integer \(k>1\) .

A weird blast took place in Andrew's dream and a certain ugly expression appeared spontaneously:

\[\dfrac{2(a_1+a_n)+5a_2-a_{n+1}}{a_3+a_4+\dots+a_{n-1}} = \dfrac{2(a_1+a_n)+5a_2-a_{n+1}}{\displaystyle\sum_{x=3}^{n-1} a_x}\]

Now your job is to find the value of above expression which randomly appeared in Andrew's sweet recursive mathematical dream.

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