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

Let $x, y, z$ be three positive real numbers in a geometric progression such that $x<y<z$. If $5 x, 16 y$, and $12 z$ are in an arithmetic progression then the common ratio of the geometric progression is

The average of a non-decreasing sequence of $N$ numbers $a_{1}, a_{2}, \ldots, a_{N}$ is $300$. If $a_{1}$ is replaced by $6 a_{1}$, the new average becomes $400$. Then, the number of possible values of $a_{1}$ is