Find an explicit formula for a sequence of the form a₁, ²₂, ²3, ... with the initial terms given below. 1 1 1 1 1 1 1 5' 2 6' 3 8' 5 10 a n = 9' 6
Find an explicit formula for a sequence of the form a₁, ²₂, ²3, ... with the initial terms given below. 1 1 1 1 1 1 1 5' 2 6' 3 8' 5 10 a n = 9' 6
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
![**Problem Statement:**
Find an explicit formula for a sequence of the form \( a_1, \, a_2, \, a_3, \ldots \) with the initial terms given below.
**Sequence:**
\[
1 - \frac{1}{5}, \quad \frac{1}{2} - \frac{1}{6}, \quad \frac{1}{3} - \frac{1}{7}, \quad \frac{1}{4} - \frac{1}{8}, \quad \frac{1}{5} - \frac{1}{9}, \quad \frac{1}{6} - \frac{1}{10}
\]
**Formula:**
\( a_n = \) _______________
**Explanation:**
The sequence consists of terms that are differences of fractions. Each term follows the pattern:
\[
a_n = \frac{1}{n} - \frac{1}{n+4}
\]
The task is to find an explicit formula for the n-th term of the sequence using this pattern.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7cff8c4a-bb33-4b54-bd2d-8ccd43ef3f82%2Faaa56db6-27c5-48d9-82f3-9a8a26dc99f5%2Fq9mmit_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find an explicit formula for a sequence of the form \( a_1, \, a_2, \, a_3, \ldots \) with the initial terms given below.
**Sequence:**
\[
1 - \frac{1}{5}, \quad \frac{1}{2} - \frac{1}{6}, \quad \frac{1}{3} - \frac{1}{7}, \quad \frac{1}{4} - \frac{1}{8}, \quad \frac{1}{5} - \frac{1}{9}, \quad \frac{1}{6} - \frac{1}{10}
\]
**Formula:**
\( a_n = \) _______________
**Explanation:**
The sequence consists of terms that are differences of fractions. Each term follows the pattern:
\[
a_n = \frac{1}{n} - \frac{1}{n+4}
\]
The task is to find an explicit formula for the n-th term of the sequence using this pattern.
Expert Solution
Step 1: Introduction to the concept:
We are asked to write what anth term will be based on the pattern given.
Step by step
Solved in 3 steps with 4 images
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education