CAT (QA) PYQs

If $x_1 = -1$ and $x_m = x_{m+1} + (m + 1)$ for every positive integer $m,$ then $x_{100}$ equals

Let the $m^{th}$ and $n^{th}$ terms of a geometric progression be $3 / 4$ and $12$, respectively, where $m<n$. If the common ratio of the progression is an integer $r$, then the smallest possible value of $r+n-m$ is

Suppose $x_{1}, x_{2}, x_{3}, \ldots, x_{100}$ are in arithmetic progression such that $x_{5}=-4$ and $2 x_{6}+2 x_{9}=x_{11}+x_{13}$, Then, $x_{100}$ equals