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

For some positive and distinct real numbers $x, y$ and $z$, if $\frac{1}{\sqrt{y}+\sqrt{z}}$ is the arithmetic mean of $\frac{1}{\sqrt{x}+\sqrt{z}}$ and $\frac{1}{\sqrt{x}+\sqrt{y}}$, then the relationship which will always hold true, is

Let $a_n$ be the $n^{th}$ term of a decreasing infinite geometric progression. If $a_1+a_2+a_3 = 52$ and $a_1a_2+a_2a_3+a_3a_1 = 624$, then the sum of this geometric progression is