CAT 2021 Progression — Previous Year Question

For a sequence of real numbers $x_1, x_2, \ldots, x_n$, if $x_1 - x_2 + x_3 - \cdots + (-1)^{\,n+1} x_n = n^2 + 2n$ for all natural numbers $n$, then the sum $x_{49} + x_{50}$ equals