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 4.2 , 3.7 , 3.2 , 2.7... ; n = 12 is 17.4 .
Given information:
The given sequence is 4.2 , 3.7 , 3.2 , 2.7... ; n = 12 .
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 terms of sequence.
Calculation:
Compute the common difference as follows,
d = a 2 − a 1 = 3.7 − 4.2 = − 0.5
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 12 for n and 4.2 for a 1 and −0.5 for d in the above formula as follows,
a 12 = 4.2 + ( 12 − 1 ) ( − 0.5 ) = 4.2 − 5.5 = − 1.3
Compute the sum of finite arithmetic sequence as follows,
S n = 12 ( 4.2 − 1.3 ) 2 = 6 ⋅ 2.9 = 17.4
Therefore, the sum of the partial arithmetic sequence is 17.4 .
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 common difference as follows,
Compute the sum of partial arithmetic sequence.
The nth term of the arithmetic sequence has the form
Substitute 12 for n and 4.2 for
Compute the sum of finite arithmetic sequence as follows,
Therefore, the sum of the partial arithmetic sequence is
Answer to Problem 62E
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 common difference as follows,
Compute the sum of partial arithmetic sequence.
The nth term of the arithmetic sequence has the form
Substitute 12 for n and 4.2 for
Compute the sum of finite arithmetic sequence as follows,
Therefore, the sum of the partial arithmetic sequence is
Chapter 8 Solutions
PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
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- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning