Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
Related questions
Question
![**Evaluate the expression.**
\[
\sum_{k=2}^{6} (115 - 6k)
\]
**Options:**
- A) 352
- B) 109
- C) 455
- D) 91
- E) 564
**Explanation:**
To evaluate the summation, we calculate each term from \(k = 2\) to \(k = 6\) and then find their total sum.
The expression inside the summation is \(115 - 6k\). We calculate it for each value of \(k\):
1. For \(k = 2\): \(115 - 6(2) = 115 - 12 = 103\)
2. For \(k = 3\): \(115 - 6(3) = 115 - 18 = 97\)
3. For \(k = 4\): \(115 - 6(4) = 115 - 24 = 91\)
4. For \(k = 5\): \(115 - 6(5) = 115 - 30 = 85\)
5. For \(k = 6\): \(115 - 6(6) = 115 - 36 = 79\)
Now, add all these calculated values:
\[103 + 97 + 91 + 85 + 79 = 455\]
The correct answer is C) 455.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F10c6527d-29e3-4038-8af3-a11cd913e02d%2Ffe795001-a0dc-4565-a78d-a482a956a9f7%2F4dynti9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Evaluate the expression.**
\[
\sum_{k=2}^{6} (115 - 6k)
\]
**Options:**
- A) 352
- B) 109
- C) 455
- D) 91
- E) 564
**Explanation:**
To evaluate the summation, we calculate each term from \(k = 2\) to \(k = 6\) and then find their total sum.
The expression inside the summation is \(115 - 6k\). We calculate it for each value of \(k\):
1. For \(k = 2\): \(115 - 6(2) = 115 - 12 = 103\)
2. For \(k = 3\): \(115 - 6(3) = 115 - 18 = 97\)
3. For \(k = 4\): \(115 - 6(4) = 115 - 24 = 91\)
4. For \(k = 5\): \(115 - 6(5) = 115 - 30 = 85\)
5. For \(k = 6\): \(115 - 6(6) = 115 - 36 = 79\)
Now, add all these calculated values:
\[103 + 97 + 91 + 85 + 79 = 455\]
The correct answer is C) 455.
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