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 $S_2$,…

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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 __________.

Accepted Answer

B - 138250. a_k b_k = (100+5j)(100-5j) = 10000 - 25j^2 for j = 0..19. Sum = 200000 - 25*2470 = 138250.

Answer

A - 137275

Answer

C - 137225

Answer

D - 135375

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 \(S_2\),…

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