CAT (QA) PYQs

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

Consider the arithmetic progression 3, 7, 11, ..... and let Aₙ denote the sum of the first n terms of this progression. Then the value of $\frac{1}{25} \sum_{n=1}^{25} A_n$ is