Evaluate: sum_(n=1)^(5)(-3x-4n) Answer:

Understand the problem: Understand the problem. We need to evaluate the sum of the expression (-3x - 4n) for n ranging from 1 to 5. This is a finite arithmetic series where n is the variable and x is considered a constant within the context of the sum.Write out the terms: Write out the terms of the sum. The sum can be written out as: (-3x - 4*1) + (-3x - 4*2) + (-3x - 4*3) + (-3x - 4*4) + (-3x - 4*5)Simplify each term: Simplify each term in the sum. Now we simplify each term: (-3x - 4) + (-3x - 8) + (-3x - 12) + (-3x - 16) + (-3x - 20)Combine like terms: Combine like terms. We can combine the constant terms and the terms with x: (-3x - 3x - 3x - 3x - 3x) + (-4 - 8 - 12 - 16 - 20) This simplifies to: -15x + (-4 - 8 - 12 - 16 - 20)Calculate sum of constants: Calculate the sum of the constant terms. Now we calculate the sum of the constant terms: -4 - 8 - 12 - 16 - 20 = -60Combine x terms: Combine the x terms with the sum of the constant terms. Now we combine the -15x term with the sum of the constant terms: -15x - 60Write final answer: Write the final answer. The final answer is the expression we have obtained: -15x - 60

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Evaluate:

sum_(n=1)^(5)(-3x-4n)
Answer:

Evaluate: $\newline$ $\sum_{n=1}^{5}(-3 x-4 n)$ $\newline$ Answer:

View step-by-step help

Home

Math Problems

Calculus

Evaluate definite integrals using the chain rule

Full solution

Q. Evaluate:

\newline

\sum_{n=1}^{5}(-3 x-4 n)

\newline

Answer:

Understand the problem: Understand the problem. $\newline$ We need to evaluate the sum of the expression $-3x - 4n$ for $n$ ranging from $1$ to $5$ . This is a finite arithmetic series where $n$ is the variable and $x$ is considered a constant within the context of the sum.
Write out the terms: Write out the terms of the sum. $\newline$ The sum can be written out as: $\newline$ $(-3x - 4\times 1) + (-3x - 4\times 2) + (-3x - 4\times 3) + (-3x - 4\times 4) + (-3x - 4\times 5)$
Simplify each term: Simplify each term in the sum. $\newline$ Now we simplify each term: $\newline$ $(-3x - 4) + (-3x - 8) + (-3x - 12) + (-3x - 16) + (-3x - 20)$
Combine like terms: Combine like terms. $\newline$ We can combine the constant terms and the terms with $x$ : $\newline$ $(-3x - 3x - 3x - 3x - 3x) + (-4 - 8 - 12 - 16 - 20)$ $\newline$ This simplifies to: $\newline$ $-15x + (-4 - 8 - 12 - 16 - 20)$
Calculate sum of constants: Calculate the sum of the constant terms. $\newline$ Now we calculate the sum of the constant terms: $\newline$ $-4 - 8 - 12 - 16 - 20 = -60$
Combine $x$ terms: Combine the $x$ terms with the sum of the constant terms. $\newline$ Now we combine the $-15x$ term with the sum of the constant terms: $\newline$ $-15x - 60$
Write final answer: Write the final answer. $\newline$ The final answer is the expression we have obtained: $\newline$ $-15x - 60$