SOLUTION: If I adding odd numbers from -7 to 101. Can you show me how to get the sum the quickest way possible?

Question 329452: If I adding odd numbers from -7 to 101. Can you show me how to get the sum the quickest way possible?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
If I adding odd numbers from -7 to 101. Can you show me how to get the sum the quickest way possible?
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-7,-5,-3.........95,97,99
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Add the 1st and the last to get 92
Add the 2nd and the next to last to get 92
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Add the 3rd and the 2nd to last to get 92
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The sum of each of the pairs is 92
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How many pairs are there?
Find the number of terms using a(n)= a(1) + (n-1)d
99 = -7+(n-1)2
106 = (n-1)2
53 = n-1
n = 54
So there are 54 terms in the series.
So there are 27 pairs of terms.
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So the sum of all the pairs is:
27*92 = 2484
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A German mathematician named Euler figured
this out in grade school.
Formula: S(n) = (n/2)(first + last)
Try it with shorter series like 1,2,3,4
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Cheers,
Stan H.

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