Concept explainers
To find: first five terms of the arithmetic sequence and the common difference. Write the nth term of the sequence as a function of n .
Answer to Problem 35RE
First five terms of the arithmetic sequence are
Common difference of the sequence is
An expression for nth term of the sequence is
Explanation of Solution
Given information:
An sequence is given with first term
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 first term.
And
First five terms of the sequence can be found by substituting 1, 2, 3, 4, and 5 for kas shown:
Hence, the first five terms of the sequence are
The common difference can be found by subtracting first term from second term.
Therefore, the common difference is
Now, the expression for nth term can be found as
Hence, the expression for nth term 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