Evaluate the sum sum_{k=1}^{11}(-13 k)

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Accepted Answer

Step:1 ：The sum (sum_{k=1}^{11}(-13 k)) is an arithmetic series with first term -13 and common difference -13.Step:2 ：The sum of an arithmetic series can be calculated using the formula (frac{n}{2}(a + l)) where n is the number of terms, a is the first term, and l is the last term.Step:3 ：In this case, n = 11, a = -13, and l = -13*11 = -143.Step:4 ：Substituting these values into the formula, we get the sum = (frac{11}{2}(-13 - 143) = -858).Step:5 ：Final Answer: The sum of the series is (boxed{-858}).

Answer

Step: 1 ：The sum (sum_{k=1}^{11}(-13 k)) is an arithmetic series with first term -13 and common difference -13.Step: 2 ：The sum of an arithmetic series can be calculated using the formula (frac{n}{2}(a + l)) where n is the number of terms, a is the first term, and l is the last term.Step: 3 ：In this case, n = 11, a = -13, and l = -13*11 = -143.Step: 4 ：Substituting these values into the formula, we get the sum = (frac{11}{2}(-13 - 143) = -858).Step: 5 ：Final Answer: The sum of the series is (boxed{-858}).

Evaluate the sum $\sum_{k=1}^{11}(-13 k)$

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