# That's it

Number Theory Level 3

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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