Sequence and Series: JEE Main 2023 Mathematics question

Let $x_{1}, x_{2}, \ldots, x_{100}$ be in an arithmetic progression, with $x_{1}=2$ and their mean equal to 200 . If $y_{i}=i\left(x_{i}-i\right), 1 \leq i \leq 100$, then the mean of $y_{1}, y_{2}, \ldots, y_{100}$ is :