Concept explainers
To find: an expression for the nth term of the arithmetic sequence for given sixth term and twelfth term.
Answer to Problem 27E
An expression for the nth term of the arithmetic sequence is
Explanation of Solution
Given information:
An sequence is given with sixth 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 sixth term.
Consider dbe the common difference and
Now, expression for sixth term will be
Now, expression for third 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
Chapter 8 Solutions
PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
- 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