IPMAT Indore (MCQ) PYQs

The sum up to $10$ terms of the series $1 \cdot 3 + 5 \cdot 7 + 9 \cdot 11 + ...$ is

The numbers $-16,2^{x+3}-2^{2 x-1}-16,2^{2 x-1}+16$ are in an arithmetic progression. Then $x$ equals ________.

The $3^{\text {rd }}, 14^{\text {th }}$ and $69^{\text {th }}$ terms of an arithmetic progression form three distinct and consecutive terms of a geometric progression. If the next term of the geometric progression is the $n^{\text {th }}$ term of the arithmetic progression, then $n$ equals ________.