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
Topic Video
Question
![**Arithmetic Sequences: Exploring the Fourteenth Term**
To grasp the concept of arithmetic sequences, let's dive into a sample problem.
**Problem Statement:**
"Find the indicated term of the arithmetic sequence."
Given Sequence:
\[ -9, -4, 1, \ldots; a_{14} \]
To find:
\[ a_{14} = ? \]
**Solution:**
First, let's identify the common difference \(d\) of the sequence:
\[
d = a_2 - a_1 = -4 - (-9) = 5
\]
The general term of an arithmetic sequence can be described by the formula:
\[
a_n = a_1 + (n - 1)d
\]
For the given sequence:
- \(a_1 = -9\)
- \(d = 5\)
We need to find \(a_{14}\):
\[
a_{14} = a_1 + (14 - 1)d
\]
Substituting the known values:
\[
a_{14} = -9 + 13 \times 5
\]
\[
a_{14} = -9 + 65
\]
\[
a_{14} = 56
\]
Thus, \(a_{14} = 56\).
**Summary:**
The fourteenth term of the arithmetic sequence \(-9, -4, 1, \ldots\) is \(56\).
By understanding the pattern and the common difference in an arithmetic sequence, we can easily find any term using the arithmetic sequence formula.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F667c2432-c02d-4ad1-9d8f-1347249c5b46%2Fade2a49f-ef89-4120-b015-68e4532620c6%2Fy5r0lz.jpeg&w=3840&q=75)
Transcribed Image Text:**Arithmetic Sequences: Exploring the Fourteenth Term**
To grasp the concept of arithmetic sequences, let's dive into a sample problem.
**Problem Statement:**
"Find the indicated term of the arithmetic sequence."
Given Sequence:
\[ -9, -4, 1, \ldots; a_{14} \]
To find:
\[ a_{14} = ? \]
**Solution:**
First, let's identify the common difference \(d\) of the sequence:
\[
d = a_2 - a_1 = -4 - (-9) = 5
\]
The general term of an arithmetic sequence can be described by the formula:
\[
a_n = a_1 + (n - 1)d
\]
For the given sequence:
- \(a_1 = -9\)
- \(d = 5\)
We need to find \(a_{14}\):
\[
a_{14} = a_1 + (14 - 1)d
\]
Substituting the known values:
\[
a_{14} = -9 + 13 \times 5
\]
\[
a_{14} = -9 + 65
\]
\[
a_{14} = 56
\]
Thus, \(a_{14} = 56\).
**Summary:**
The fourteenth term of the arithmetic sequence \(-9, -4, 1, \ldots\) is \(56\).
By understanding the pattern and the common difference in an arithmetic sequence, we can easily find any term using the arithmetic sequence formula.
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.Recommended textbooks for you
![Algebra and Trigonometry (6th Edition)](https://www.bartleby.com/isbn_cover_images/9780134463216/9780134463216_smallCoverImage.gif)
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
![Contemporary Abstract Algebra](https://www.bartleby.com/isbn_cover_images/9781305657960/9781305657960_smallCoverImage.gif)
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
![Linear Algebra: A Modern Introduction](https://www.bartleby.com/isbn_cover_images/9781285463247/9781285463247_smallCoverImage.gif)
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
![Algebra and Trigonometry (6th Edition)](https://www.bartleby.com/isbn_cover_images/9780134463216/9780134463216_smallCoverImage.gif)
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
![Contemporary Abstract Algebra](https://www.bartleby.com/isbn_cover_images/9781305657960/9781305657960_smallCoverImage.gif)
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
![Linear Algebra: A Modern Introduction](https://www.bartleby.com/isbn_cover_images/9781285463247/9781285463247_smallCoverImage.gif)
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
![Algebra And Trigonometry (11th Edition)](https://www.bartleby.com/isbn_cover_images/9780135163078/9780135163078_smallCoverImage.gif)
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
![Introduction to Linear Algebra, Fifth Edition](https://www.bartleby.com/isbn_cover_images/9780980232776/9780980232776_smallCoverImage.gif)
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
![College Algebra (Collegiate Math)](https://www.bartleby.com/isbn_cover_images/9780077836344/9780077836344_smallCoverImage.gif)
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education