(a)
To find: The first term of an arithmetic sequence for the given problem.
(a)
Answer to Problem 52RE
The first term of an arithmetic sequence is
Explanation of Solution
Given information: Second and sixth term of arithmetic sequence are
Formula used :
of the arithmetic sequence respectively.
Calculation:
Substitute
Since the second term is
Now, Substitute
Since the sixth term is
Multiply equation (1) by 5 and subtract the resulting equation from equation (2) to obtain the required result.
Therefore, the first term of an arithmetic sequence is
(b)
To find: The common difference for the given problem.
(b)
Answer to Problem 52RE
The common difference is
Explanation of Solution
Given information: Second and sixth term of arithmetic sequence are
Formula used :
of the arithmetic sequence respectively.
Calculation:
Substitute
Since the second term is
Now, Substitute
Since the sixth term is
Subtract equation (1) from equation (2) and simplify to obtain the required result.
Therefore, the common difference is
(c)
To find: An explicit formula for the
(c)
Answer to Problem 52RE
An explicit formula for the
Explanation of Solution
Given information: Second and sixth term of arithmetic sequence are
Formula used :
of the geometric sequence respectively.
Calculation:
From part (a) and part (b) the first term and the common difference are
Substitute
Therefore, explicit formula for the given problem is
Chapter 8 Solutions
CALCULUS:GRAPHICAL,...,AP ED.-W/ACCESS
- 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