Concept explainers
To find: first five terms of the arithmetic sequencefor given third term and 15th term.
. Verify the result graphically.
Answer to Problem 37E
First five terms of the arithmetic sequence are
Explanation of Solution
Given information:
An sequence is given with third 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 third term and the 15th term.
Consider dbe the common difference and
Now, expression for third term will be
Now, expression for 15th term will be
Subtract equation (1) from equation (2) to find the common difference.
Now, the first term can be found by substituting
So, the nth term of the arithmetic sequence can be found as
Thus, the expression for the nth term of the arithmetic sequence is
First five terms of the sequence can be found as shown:
Hence, the first five terms of the sequence are
Use the table feature of graphing utility to find the first 5 terms of sequence by using following steps:
Press MODE key, select Seq in the fourth line and hit Enter
Press
Set the table by pressing TBLSET and then press TABLE
Hence, the result is verified.
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