IPMAT Indore 2025 — Question 17

Let $S_1=\{100,105,110,115,\dots \}$ and $S_2=\{100,95,90,85,\dots \}$ 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