CAT (QA) PYQs

If the population of a town is $p$ in the beginning of any year then it becomes $3+2 p$ in the beginning of the next year. If the population in the beginning of $2019$ is $1000$ then the population in the beginning of $2034$ will be

Let $t_1, t_2, \dots$ be real numbers such that $t_1 + t_2 +\dots+ t_n = 2n^2 + 9n + 13$, for every positive integer $n\ge2$. If $t_k =103$, then $k$ equals

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