Evaluate the summation below. Answer: 5 Σ(-2n + 3n) n=2 Submit Answe.
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
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Question
![The task is to evaluate the summation below:
\[
\sum_{n=2}^{5} (-2n^2 + 3n)
\]
To evaluate this, calculate the expression \(-2n^2 + 3n\) for each integer value of \(n\) from 2 to 5, and then find the sum of these values.
**Steps:**
1. **For \(n = 2\):**
\[
-2(2)^2 + 3(2) = -8 + 6 = -2
\]
2. **For \(n = 3\):**
\[
-2(3)^2 + 3(3) = -18 + 9 = -9
\]
3. **For \(n = 4\):**
\[
-2(4)^2 + 3(4) = -32 + 12 = -20
\]
4. **For \(n = 5\):**
\[
-2(5)^2 + 3(5) = -50 + 15 = -35
\]
Finally, add all these results together:
\[
-2 + (-9) + (-20) + (-35) = -66
\]
The evaluated result of the summation is \(-66\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2f703597-d7fa-4c88-9f36-657b48839e33%2F7bcbc1ff-883e-4c99-905e-3d35d427f941%2Fm3sss5_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The task is to evaluate the summation below:
\[
\sum_{n=2}^{5} (-2n^2 + 3n)
\]
To evaluate this, calculate the expression \(-2n^2 + 3n\) for each integer value of \(n\) from 2 to 5, and then find the sum of these values.
**Steps:**
1. **For \(n = 2\):**
\[
-2(2)^2 + 3(2) = -8 + 6 = -2
\]
2. **For \(n = 3\):**
\[
-2(3)^2 + 3(3) = -18 + 9 = -9
\]
3. **For \(n = 4\):**
\[
-2(4)^2 + 3(4) = -32 + 12 = -20
\]
4. **For \(n = 5\):**
\[
-2(5)^2 + 3(5) = -50 + 15 = -35
\]
Finally, add all these results together:
\[
-2 + (-9) + (-20) + (-35) = -66
\]
The evaluated result of the summation is \(-66\).
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