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

Let $x, y, z$ be three positive real numbers in a geometric progression such that $x<y<z$. If $5 x, 16 y$, and $12 z$ are in an arithmetic progression then the common ratio of the geometric progression is

If $(2n + 1) + (2n + 3) + (2n + 5) + .... + (2n + 47) = 5280$, then what is the value of $1 + 2 + 3 + ... + n$?