CAT (QA) PYQs

Let $a_n$ be the $n^{th}$ term of a decreasing infinite geometric progression. If $a_1+a_2+a_3 = 52$ and $a_1a_2+a_2a_3+a_3a_1 = 624$, then the sum of this geometric progression is

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

In an arithmetic progression, if the sum of fourth, seventh and tenth terms is 99, and the sum of the first fourteen terms is 497, then the sum of first five terms is