Recursive sequence

Algebra Level 4

We define a recursive sequence of natural numbers such that a1=2a_{1}=2 and an+1=3an+2a_{n+1}=3a_{n}+2 for n1n\geq1. Find [2n=1100an]+200a100\frac{[2\sum_{n=1}^{100}a_{n}]+200}{a_{100}}.

The problem is original.

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