Evaluate the summation below. 5sum_(t=2)^(5)(7-3t) Answer:

Write Terms Explicitly: Write out the terms of the summation explicitly. The summation 5sum_(t=2)^(5)(7-3t) means we need to evaluate (7-3t) for each integer value of t from 2 to 5, and then multiply the sum of these terms by 5.Calculate Each Term: Calculate each term of the summation. For t=2: (7-3*2) = 7-6 = 1 For t=3: (7-3*3) = 7-9 = -2 For t=4: (7-3*4) = 7-12 = -5 For t=5: (7-3*5) = 7-15 = -8Add Terms Together: Add the terms of the summation together. Sum = 1 + (-2) + (-5) + (-8) = 1 - 2 - 5 - 8 = -14Multiply by 5: Multiply the sum by 5. Final Answer = 5 * (-14) = -70

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Evaluate the summation below.

5sum_(t=2)^(5)(7-3t)
Answer:

Evaluate the summation below. $\newline$ $5 \sum_{t=2}^{5}(7-3 t)$ $\newline$ Answer:

View step-by-step help

Home

Math Problems

Algebra 2

Sum of finite series starts from 1

Full solution

Q. Evaluate the summation below.

\newline

5 \sum_{t=2}^{5}(7-3 t)

\newline

Answer:

Write Terms Explicitly: Write out the terms of the summation explicitly. $\newline$ The summation $5\sum_{t=2}^{5}(7-3t)$ means we need to evaluate $(7-3t)$ for each integer value of $t$ from $2$ to $5$ , and then multiply the sum of these terms by $5$ .
Calculate Each Term: Calculate each term of the summation. $\newline$ For $t=2$ : $(7-3\times 2) = 7-6 = 1$ $\newline$ For $t=3$ : $(7-3\times 3) = 7-9 = -2$ $\newline$ For $t=4$ : $(7-3\times 4) = 7-12 = -5$ $\newline$ For $t=5$ : $(7-3\times 5) = 7-15 = -8$
Add Terms Together: Add the terms of the summation together. $\newline$ Sum = $1 + (-2) + (-5) + (-8) = 1 - 2 - 5 - 8 = -14$
Multiply by $5$ : Multiply the sum by $5$ . $\newline$ Final Answer = $5 \times (-14) = -70$