CAT (QA) PYQs

Let $a_1, a_2, ...$ be integers such that $a_1 - a_2 + a_3 - a_4 + ... + (-1)^{n - 1} a_n = n$, for all $n \ge 1$. Then $a_{51} + a_{52} + ... + a_{1023}$ equals

The average of all 3-digit terms in the arithmetic progression $38, 55, 72, \dots$, is

Let $a_n$ and $b_n$ be two sequences such that $a_n = 13 + 6 (n - 1)$ and $b_n = 15 + 7 (n - 1)$ for all natural numbers $n$. Then, the largest three digit integer that is common to both these sequences, is