Find the sum. sum_(k=1)^(50)(131-4k)=

Understand the series: Understand the series and its general term. The series is the sum of terms of the form (131-4k) where k takes on integer values from 1 to 50. We need to find the sum of all these terms.Calculate first term: Calculate the first term of the series. Substitute k=1 into the general term to find the first term. First term = 131 - 4(1) = 131 - 4 = 127Calculate last term: Calculate the last term of the series. Substitute k=50 into the general term to find the last term. Last term = 131 - 4(50) = 131 - 200 = -69Calculate sum of series: Calculate the sum of the arithmetic series. The sum of an arithmetic series can be found using the formula: Sum = (n/2) * (first term + last term) where n is the number of terms. In this case, n=50. Sum = (50/2) * (127 - 69)Perform calculations: Perform the calculations to find the sum. Sum = 25 * (127 - 69) = 25 * 58 = 1450

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Find the sum. $\newline$ $\sum_{k=1}^{50}(131-4 k)=$

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Algebra 2

Composition of linear and quadratic functions: find a value

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Q. Find the sum.

\newline

\sum_{k=1}^{50}(131-4 k)=

Understand the series: Understand the series and its general term. $\newline$ The series is the sum of terms of the form $(131-4k)$ where $k$ takes on integer values from $1$ to $50$ . We need to find the sum of all these terms.
Calculate first term: Calculate the first term of the series. $\newline$ Substitute $k=1$ into the general term to find the first term. $\newline$ First term = $131 - 4(1) = 131 - 4 = 127$
Calculate last term: Calculate the last term of the series. $\newline$ Substitute $k=50$ into the general term to find the last term. $\newline$ Last term = $131 - 4(50) = 131 - 200 = -69$
Calculate sum of series: Calculate the sum of the arithmetic series. $\newline$ The sum of an arithmetic series can be found using the formula: $\newline$ Sum $= \frac{n}{2} \times (\text{first term} + \text{last term})$ $\newline$ where $n$ is the number of terms. In this case, $n=50$ . $\newline$ Sum $= \frac{50}{2} \times (127 - 69)$
Perform calculations: Perform the calculations to find the sum. $\newline$ Sum = $25 \times (127 - 69) = 25 \times 58 = 1450$