IPMAT Indore 2019 (MCQ) PYQs

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

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 sum of the first 15 terms in an arithmetic progression is 200, while the sum of the next 15 terms is 350. Then the common difference is