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rearrange S= n/2 [ 2a+ (n-1)d ] to get a. please show working
get a on its ownS= n/2 [ 2a+ (n-1)d ]
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- By laura3005 |
- Category: calculus |
- Grade level: 11th grade (17)
- Aug/07/2008 |
- Answers to this question: 3
Answer by: Dr.Maths
First Answer
Solution:
Given: S=n/2[2a+(n-1)d] ...............(1)
Equation (1) can be written as,
S=na + n(n-1)d/2
===> S-n(n-1)d/2 =na
===> S/n -(n-1)d/2 =a ( divide both sides by n.)
===> a= [2S - n(n-1)d]/2n
Answer: a= [2S - n(n-1)d]/2n
Given: S=n/2[2a+(n-1)d] ...............(1)
Equation (1) can be written as,
S=na + n(n-1)d/2
===> S-n(n-1)d/2 =na
===> S/n -(n-1)d/2 =a ( divide both sides by n.)
===> a= [2S - n(n-1)d]/2n
Answer: a= [2S - n(n-1)d]/2n
- Aug/07/2008 |
- Answers by Dr.Maths: 57 |
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Answer by: sreenu_nampa
Best Answerwe have
S= n/2 [ 2a+ (n-1)d ]
take the cross product
2S = n[ 2a+ (n-1)d ]
2S = 2an + n(n-1)d ( using left distributive law)
2S - n(n-1)d = 2an
2an = 2S - n(n-1)d
a = 1 [2S - n(n-1)d]
2n
- Aug/07/2008 |
- Answers by sreenu_nampa: 124 |
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Answer by: Ganesha
Question:
rearrange S= n/2 [ 2a+ (n-1)d ] to get a. please show working
get a on its own S= n/2 [ 2a+ (n-1)d ].
Solution:
(Two of our MindZinger experts answered. I agree with both for their contribution.)
Please think that you are given the values of S, n, d and this equation which relates
S,n ,a and d . Now you have to find the value of a .
Here we treat a , as an unknown and find its value through the other known values of S,n and d.
The method of finding a is quite well expressed already and I repeat below :
S = (n/2)[2 a +(n-1)d], Given. divide both sides by n/2 to get,
S*(2/n) = 2a + (n-1)d. Subtract (n-1)d from both sides to get,
(2S/n ) -(n-1)d = 2 a. Thus,
a = (S/n) - (n-1)d/2.
- Aug/08/2008 |
- Answers by Ganesha: 1193 |
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