CAT (QA) PYQs

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

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

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