Evaluate: sum_(n=2)^(6)(nx-3) Answer:

Substitute n values: We are asked to evaluate the sum of the expression (nx - 3) as n varies from 2 to 6. This means we will substitute n with each integer from 2 to 6 into the expression, calculate the value, and then sum all the results together.Calculate terms: First, substitute n = 2 into the expression (nx - 3) to get the first term of the sum. 2x - 3Add all terms: Next, substitute n = 3 into the expression (nx - 3) to get the second term of the sum. 3x - 3Combine like terms: Then, substitute n = 4 into the expression (nx - 3) to get the third term of the sum. 4x - 3Simplify terms: After that, substitute n = 5 into the expression (nx - 3) to get the fourth term of the sum. 5x - 3Calculate sum: Finally, substitute n = 6 into the expression (nx - 3) to get the fifth term of the sum. 6x - 3Now, add all the terms together to find the sum. (2x - 3) + (3x - 3) + (4x - 3) + (5x - 3) + (6x - 3)Combine like terms by adding all the x terms together and all the constant terms together. 2x + 3x + 4x + 5x + 6x - 3 - 3 - 3 - 3 - 3Simplify the x terms and the constant terms. (2x + 3x + 4x + 5x + 6x) - (3 + 3 + 3 + 3 + 3)Calculate the sum of the x terms and the sum of the constants. 20x - 15

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Evaluate: $\newline$ $\sum_{n=2}^{6}(n x-3)$ $\newline$ Answer:

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Algebra 2

Simplify variable expressions using properties

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Q. Evaluate:

\newline

\sum_{n=2}^{6}(n x-3)

\newline

Answer:

Substitute $n$ values: We are asked to evaluate the sum of the expression $(nx - 3)$ as $n$ varies from $2$ to $6$ . This means we will substitute $n$ with each integer from $2$ to $6$ into the expression, calculate the value, and then sum all the results together.
Calculate terms: First, substitute $n = 2$ into the expression $(nx - 3)$ to get the first term of the sum. $2x - 3$
Add all terms: Next, substitute $n = 3$ into the expression $(nx - 3)$ to get the second term of the sum. $3x - 3$
Combine like terms: Then, substitute $n = 4$ into the expression $(nx - 3)$ to get the third term of the sum. $4x - 3$
Simplify terms: After that, substitute $n = 5$ into the expression $(nx - 3)$ to get the fourth term of the sum. $5x - 3$
Calculate sum: Finally, substitute $n = 6$ into the expression $(nx - 3)$ to get the fifth term of the sum. $6x - 3$
Calculate sum: Finally, substitute $n = 6$ into the expression $(nx - 3)$ to get the fifth term of the sum. $6x - 3$ Now, add all the terms together to find the sum. $(2x - 3) + (3x - 3) + (4x - 3) + (5x - 3) + (6x - 3)$
Calculate sum: Finally, substitute $n = 6$ into the expression $(nx - 3)$ to get the fifth term of the sum. $6x - 3$ Now, add all the terms together to find the sum. $(2x - 3) + (3x - 3) + (4x - 3) + (5x - 3) + (6x - 3)$ Combine like terms by adding all the $x$ terms together and all the constant terms together. $2x + 3x + 4x + 5x + 6x - 3 - 3 - 3 - 3 - 3$
Calculate sum: Finally, substitute $n = 6$ into the expression $(nx - 3)$ to get the fifth term of the sum. $6x - 3$ Now, add all the terms together to find the sum. $(2x - 3) + (3x - 3) + (4x - 3) + (5x - 3) + (6x - 3)$ Combine like terms by adding all the $x$ terms together and all the constant terms together. $2x + 3x + 4x + 5x + 6x - 3 - 3 - 3 - 3 - 3$ Simplify the $x$ terms and the constant terms. $(2x + 3x + 4x + 5x + 6x) - (3 + 3 + 3 + 3 + 3)$
Calculate sum: Finally, substitute $n = 6$ into the expression $(nx - 3)$ to get the fifth term of the sum. $6x - 3$ Now, add all the terms together to find the sum. $(2x - 3) + (3x - 3) + (4x - 3) + (5x - 3) + (6x - 3)$ Combine like terms by adding all the $x$ terms together and all the constant terms together. $2x + 3x + 4x + 5x + 6x - 3 - 3 - 3 - 3 - 3$ Simplify the $x$ terms and the constant terms. $(2x + 3x + 4x + 5x + 6x) - (3 + 3 + 3 + 3 + 3)$ Calculate the sum of the $x$ terms and the sum of the constants. $20x - 15$