CAT (QA) PYQs

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

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

An infinite geometric progression $a_1, a_2, a_3,...$ has the property that $a_n = 3(a_{n+1} + a_{n+2} +....)$ for every $n \ge 1$. If the sum $a_1 + a_2 + a_3 +..... = 32$, then $a_5$ is