CAT (QA) PYQs

An infinite geometric progression $a_1, a_2, a_3,...$ has the property that $a_n = 3(a_{n+1} + a_{n+2} +....)$ for every $n \ge 1$. If the sum $a_1 + a_2 + a_3 +..... = 32$, then $a_5$ is

For a sequence of real numbers $x_1, x_2, ...... x_n$, if $x_1 - x_2 + x_3 - .... + (-1)^{n + 1} x_n = n^2 + 2n$ for all natural numbers n, then the sum $x_{49} + x_{50}$ equals

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