IPMAT Indore (MCQ) PYQs

A person standing at the centre of an open ground first walks 32 meters towards the east, takes a right turn and walks 16 meters, takes another right turn and walks 8 meters, and so on. How far will the person be from the original starting point after an infinite number of such walks in this pattern?

Let $S_1 = \{100, 105, 110, 115, ... \}$ and $S_2 = \{100, 95, 90, 85, ... \}$ be two series in arithmetic progression. If $a_k$ and $b_k$ are the $k$-th terms of $S_1$ and $S_2$, respectively, then $\sum_{k=1}^{20} a_k b_k$ 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 ________.