Concept explainers
To write: the first five terms of the given sequence. Whether the given sequence is an arithmetic sequence. The common difference for an arithmetic sequence.
Answer to Problem 20E
The first five terms of the given sequence are
The given sequence is an arithmetic sequence.
The common difference of the arithmetic sequence is
Explanation of Solution
Given information:
An sequence as
Concept used:
An arithmetic sequence of n terms, has the form
That is
Common difference can be defined by d .
nth term of the arithmetic sequence has the form
Where
Calculation:
Now, consider the given sequence.
First five terms of the sequence can be found by substituting 1, 2, 3, 4, and 5 for nas shown:
Hence, the first five terms of the sequence are
Now, the difference can be calculated as shown:
Now, the differences for each two consecutive terms are as
Therefore, differences are common for each two consecutive terms of the sequence.
So, it is an arithmetic sequence.
And, the common difference of the arithmetic sequence is
Chapter 8 Solutions
Precalculus with Limits: A Graphing Approach
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning