CAT (QA) PYQs

Let $a_1, a_2, a_3, a_4, a_5$ be a sequence of five consecutive odd numbers. Consider a new sequence of five consecutive even numbers ending with $2a_3$.

If the sum of the numbers in the new sequence is $450$, then $a_5$ is

Let the $m^{th}$ and $n^{th}$ terms of a geometric progression be $3 / 4$ and $12$, respectively, where $m<n$. If the common ratio of the progression is an integer $r$, then the smallest possible value of $r+n-m$ is

If $(2n + 1) + (2n + 3) + (2n + 5) + .... + (2n + 47) = 5280$, then what is the value of $1 + 2 + 3 + ... + n$?