101 101 Suppose that Σ ai = -12 and Σ bi = -19. i=1 i=1 Compute the sum. 101 Σ( – 5ai

asked Mar 26, 2023 84.2k views

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101 101 Suppose that Σ ai = -12 and Σ bi = -19. i=1 i=1 Compute the sum. 101 Σ( – 5ai – 12bi) i=1

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Distribute the summation over the sum.

$\displaystyle \sum_(i=1)^(101) (-5a_i - 12b_i) = -5 \sum_(i=1)^(101) a_i - 12 \sum_(i=1)^(101) b_i$

Now plug in the known sums and simplify.

$\displaystyle \sum_(i=1)^(101) (-5a_i - 12b_i) = -5(-12) - 12(-19) = \boxed{288}$

Anayansi answered Mar 31, 2023