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,...
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![**Question:**
Find the arithmetic series of the arithmetic sequence: \(5, 7, 9, \ldots, 301\).
**Options:**
- a) 765
- b) 22,496
- c) 22,797
- d) 23,098
**Explanation:**
This question asks for the sum of the numbers in the arithmetic sequence that begins with 5 and ends with 301. The common difference between terms is 2, as each term increases by 2 from the previous term. To find the arithmetic series, one can use the formula for the sum \(S_n\) of an arithmetic series:
\[ S_n = \frac{n}{2} (a + l) \]
where \(n\) is the number of terms, \(a\) is the first term, and \(l\) is the last term. To find \(n\), use the formula for the \(n\)-th term of an arithmetic sequence:
\[ a_n = a + (n-1)d \]
where \(d\) is the common difference. Here, solve for \(n\) when \(a_n = 301\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff2a26d62-f5b2-42c9-9720-1adbdcac00ca%2Fa3759512-da99-4469-9bf9-784d88809429%2Fe1tg1x_processed.png&w=3840&q=75)
Transcribed Image Text:**Question:**
Find the arithmetic series of the arithmetic sequence: \(5, 7, 9, \ldots, 301\).
**Options:**
- a) 765
- b) 22,496
- c) 22,797
- d) 23,098
**Explanation:**
This question asks for the sum of the numbers in the arithmetic sequence that begins with 5 and ends with 301. The common difference between terms is 2, as each term increases by 2 from the previous term. To find the arithmetic series, one can use the formula for the sum \(S_n\) of an arithmetic series:
\[ S_n = \frac{n}{2} (a + l) \]
where \(n\) is the number of terms, \(a\) is the first term, and \(l\) is the last term. To find \(n\), use the formula for the \(n\)-th term of an arithmetic sequence:
\[ a_n = a + (n-1)d \]
where \(d\) is the common difference. Here, solve for \(n\) when \(a_n = 301\).
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