That's it

Suppose \(a_1,a_2,\ldots,a_{200} \) are integers arranged on a circle such that \(\displaystyle a_n= \frac{a_{n-1} + a_{n+1}}2 \) and \(\displaystyle \sum_{n=1}^{100} a_{2n} = 1234 \). Find the value of \(\displaystyle \sum_{n=1}^{200} a_n \).

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