Recursive sequence

Algebra Level 4

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

The problem is original.

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