CAT (QA) PYQs

Consider the sequence $t_1 = 1$, $t_2 = -1$ and $t_n = \left(\frac{n-3}{n-1}\right) t_{n-2}$ for $n \ge 3$. The, the value of the sum $\frac{1}{t_2} + \frac{1}{t_4} + \frac{1}{t_6} + \dots + \frac{1}{t_{2022}} + \frac{1}{t_{2024}}$ is

Suppose $x_{1}, x_{2}, x_{3}, \ldots, x_{100}$ are in arithmetic progression such that $x_{5}=-4$ and $2 x_{6}+2 x_{9}=x_{11}+x_{13}$, Then, $x_{100}$ equals

If $a_{1}, a_{2} \ldots .$. are in A.P., then, $\frac{1}{\sqrt{a_{1}}+\sqrt{a_{2}}}+\frac{1}{\sqrt{a_{2}}+\sqrt{a_{3}}}+\ldots .+\frac{1}{\sqrt{a_{n}}+\sqrt{a_{n+1}}}$ is equal to