CAT (QA) PYQs

The sum of the infinite series is $\frac{1}{5}\left(\frac{1}{5}-\frac{1}{7}\right)+\left(\frac{1}{5}\right)^{2}\left(\left(\frac{1}{5}\right)^{2}-\left(\frac{1}{7}\right)^{2}\right)+\left(\frac{1}{5}\right)^{3}\left(\left(\frac{1}{5}\right)^{3}-\left(\frac{1}{7}\right)^{3}\right)+\ldots .$. equal to

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

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