CAT (QA) PYQs

Consider a sequence of real number $x_1, x_2, x_3, ...$ such that $x_{n+1} = x_n + n - 1$ for all $n \ge 1$. If $x_1 = -1$ then $x_{100}$ is equal to

If $a_1 + a_2 + a_3 + \dots + a_n = 3 \times (2^{n+1} - 2)$, for every $n \ge 1$, then $a_{11}$ 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