Concept explainers
To calculate: The sum of the arithmetic sequence of the nth partial for
integer from −10 to 50.
The sum of the partial arithmetic sequence 0 , − 9 , − 18 , − 27 , ... , n = 40 is − 7020 .
Given information:
The given sequence is 0 , − 9 , − 18 , − 27 , ... , n = 40 .
Definition used:
The nth term of the arithmetic sequence has the form a n = a 1 + ( n − 1 ) d ,where a 1 is the first term of the sequence, and d is the common difference.
The sum of finite arithmetic sequence is given by S n = n ( a 1 + a n ) 2 .
Here n is the number of terms, a 1 is the first term of the sequence, and a n is the last tems of sequence.
Calculation:
Compute the sum of partial arithmetic sequence.
The nth term of the arithmetic sequence has the form a n = a 1 + ( n − 1 ) d .
Substitute 40 for n and 0 for a 1 and −9 for d in the above formula as follows,
a 40 = 0 + ( 40 − 1 ) ( − 39 ) = 0 + 39 ( − 9 ) − 351
Compute the sum of finite arithmetic sequence as follows,
S n = 40 ( 0 + ( − 351 ) ) 2 = − 7020
Therefore, the sum of the partial arithmetic sequenceis − 7020 .
The sum of the partial arithmetic sequence
Given information:
The given sequence is
Definition used:
The nth term of the arithmetic sequence has the form
The sum of finite arithmetic sequence is given by
Here n is the number of terms,
Calculation:
Compute the sum of partial arithmetic sequence.
The nth term of the arithmetic sequence has the form
Substitute 40 for n and 0 for
Compute the sum of finite arithmetic sequence as follows,
Therefore, the sum of the partial arithmetic sequenceis
Answer to Problem 61E
The sum of the partial arithmetic sequence
Explanation of Solution
Given information:
The given sequence is
Definition used:
The nth term of the arithmetic sequence has the form
The sum of finite arithmetic sequence is given by
Here n is the number of terms,
Calculation:
Compute the sum of partial arithmetic sequence.
The nth term of the arithmetic sequence has the form
Substitute 40 for n and 0 for
Compute the sum of finite arithmetic sequence as follows,
Therefore, the sum of the partial arithmetic sequenceis
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