CAT (QA) PYQs

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

Three positive integers $x, y$ and $z$ are in arithmetic progression. If $y − x > 2$ and $xyz = 5(x + y + z)$, then $z − x$ equals

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