CAT (QA) PYQs

If the square of the $7$th term of an arithmetic progression with positive common difference equals the product of the $3$rd and $17$th terms, then the ratio of the first term to the common difference is

For any natural number n, suppose the sum of the first n terms of an arithmetic progression is $(n + 2n^2)$. If the $n^{th}$ term of the progression is divisible by $9$, then the smallest possible value of $n$ is

If $\mathrm{x}_{0}=1, \mathrm{x}_{1}=2$, and $\mathrm{x}_{\mathrm{n}+2}=\frac{1+x_{n+1}}{x_{n}}, n=0,1,2,3 \ldots \ldots$., then $x_{2021}$ is