Concept explainers
To find The sum of the integer from −10 to 50.
The sum of the integerfrom −10 to 50 is 1220 .
Given information:
Integers from −10 to 50.
Definition used:
An arithmetic sequence of n terms has the form a 1 , a 2 , a 3 , ⋯ , a n and should be have a common difference between between each two consecutive terms which is given by,
a 2 − a 1 = a 3 − a 2 = a 4 − a 3 = … = a n − a n − 1
The common difference can be defined by d is a 2 − a 1 = a 3 − a 2 = a 4 − a 3 = … = a n − a n − 1 = d
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.
Sum of an arithmetic finite sequence has the form S n = n 2 ( a 1 + a n ) .
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:
Find the sum of integers from −10 to 50.
The sequence will of the form − 10 , − 9 , − 8 , .. , 0 , 1 , 2 , 3 , .. , 50 .
Compute the common difference as follows,
d = a 2 − a 1 = − 9 − ( − 10 ) = − 9 + 10 = 1
So, the number of terms of the sequence will be,
a n = a 1 + ( n − 1 ) d 50 = − 10 + ( n − 1 ) ( 1 ) 50 = − 10 + n − 1 n = 61
Therefore, the sum of the finite sequence is calculated as follows,
S n = n 2 ( a 1 + a n ) = 61 2 ( − 10 + 50 ) = 61 ⋅ ( 20 ) = 1220
Therefore, the sum of the integers from −10 or 50 is 1220 .
The sum of the integerfrom −10 to 50 is
Given information:
Integers from −10 to 50.
Definition used:
An arithmetic sequence of n terms has the form
The common difference can be defined by d is
nth term of the arithmetic sequence has the form
Sum of an arithmetic finite sequence has the form
Here n is the number of terms,
Calculation:
Find the sum of integers from −10 to 50.
The sequence will of the form
Compute the common difference as follows,
So, the number of terms of the sequence will be,
Therefore, the sum of the finite sequence is calculated as follows,
Therefore, the sum of the integers from −10 or 50 is
Answer to Problem 60E
The sum of the integerfrom −10 to 50 is
Explanation of Solution
Given information:
Integers from −10 to 50.
Definition used:
An arithmetic sequence of n terms has the form
The common difference can be defined by d is
nth term of the arithmetic sequence has the form
Sum of an arithmetic finite sequence has the form
Here n is the number of terms,
Calculation:
Find the sum of integers from −10 to 50.
The sequence will of the form
Compute the common difference as follows,
So, the number of terms of the sequence will be,
Therefore, the sum of the finite sequence is calculated as follows,
Therefore, the sum of the integers from −10 or 50 is
Chapter 8 Solutions
PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
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