Evaluate: sum_(n=1)^(4)(nx-5) Answer:

Understand the expression: Understand the expression The expression sum_(n=1)^(4)(nx-5) means we need to calculate the sum of the terms (nx-5) for each integer value of n from 1 to 4.Calculate for n=1: Calculate the term for n=1 For n=1, the term is (1x-5).Calculate for n=2: Calculate the term for n=2 For n=2, the term is (2x-5).Calculate for n=3: Calculate the term for n=3 For n=3, the term is (3x-5).Calculate for n=4: Calculate the term for n=4 For n=4, the term is (4x-5).Add all terms: Add all the terms together Now we add all the terms from n=1 to n=4: (1x-5) + (2x-5) + (3x-5) + (4x-5)Combine like terms: Combine like terms Combine the x terms and the constant terms separately: (1x + 2x + 3x + 4x) - (5 + 5 + 5 + 5)Simplify the expression: Simplify the expression Simplify the x terms and the constant terms: 10x - 20

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Algebra 2

Evaluate rational expressions II

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Q. Evaluate:

\newline

\sum_{n=1}^{4}(n x-5)

\newline

Answer:

Understand the expression: Understand the expression $\newline$ The expression $\sum_{n=1}^{4}(nx-5)$ means we need to calculate the sum of the terms $(nx-5)$ for each integer value of $n$ from $1$ to $4$ .
Calculate for $n=1$ : Calculate the term for $n=1$ For $n=1$ , the term is $(1x-5)$ .
Calculate for $n=2$ : Calculate the term for $n=2$ For $n=2$ , the term is $(2x-5)$ .
Calculate for $n=3$ : Calculate the term for $n=3$ For $n=3$ , the term is $(3x-5)$ .
Calculate for $n=4$ : Calculate the term for $n=4$ For $n=4$ , the term is $(4x-5)$ .
Add all terms: Add all the terms together $\newline$ Now we add all the terms from $n=1$ to $n=4$ : $\newline$ $(1x-5) + (2x-5) + (3x-5) + (4x-5)$
Combine like terms: Combine like terms $\newline$ Combine the $x$ terms and the constant terms separately: $\newline$ $(1x + 2x + 3x + 4x) - (5 + 5 + 5 + 5)$
Simplify the expression: Simplify the expression Simplify the $x$ terms and the constant terms: $10x - 20$