Find the arithmetic series of the arithmetic sequence: (5, 7, 9, ., 301}. a 765 b 22,496 22,797 d 23,098

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,...
icon
Related questions
Question
**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 \(a_n = 301\).
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 \(a_n = 301\).
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education