CAT (QA) PYQs

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

Let $t_1, t_2, \dots$ be real numbers such that $t_1 + t_2 +\dots+ t_n = 2n^2 + 9n + 13$, for every positive integer $n\ge2$. If $t_k =103$, then $k$ equals

Consider the arithmetic progression 3, 7, 11, ..... and let Aₙ denote the sum of the first n terms of this progression. Then the value of $\frac{1}{25} \sum_{n=1}^{25} A_n$ is