# A Special Sequence - For my Friend Sharky Kesa!

Algebra Level 4

A sequence of numbers $x_{1},x_{2},\ldots ,x_{100}$ has the property that for every integer $k$ between 1 and 100 inclusive the number $x_{k}$ is $k$ less than the sum of other 99 numbers. Given that $x_{50}=\dfrac mn$, where $m$ and $n$ are relatively prime positive integer, find $m+n$.

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