CAT (QA) PYQs

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

If the square of the $7$th term of an arithmetic progression with positive common difference equals the product of the $3$rd and $17$th terms, then the ratio of the first term to the common difference is