Question 285284: Explain how you would find the sum of the first 50 even numbers.What is the sum? Found 2 solutions by stanbon, Edwin McCravy:Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! Explain how you would find the sum of the first 50 even numbers.What is the sum?
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2+4+6+....+100
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S(n) = (n/2)(A+L)
S(50) = (50/2)(2+100)
S(50) = 25*102
S(50) = 2550
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Cheers,
Stan H.
Either of two ways:
Let the sum be S. Then write these two equivalent equations
and add them:
S = 2 + 4 + 6 + 8 + 10 + ''' + 92 + 94 + 96 + 98 + 100
S = 100 + 98 + 96 + 94 + 92 + ''' + 10 + 8 + 6 + 4 + 2
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2S = 102 + 102 + 102 + 102 + 102 + ''' + 102 + 102 + 102 + 102 + 102
There are 50 terms on the right, so the right side is 50*102
or 2550, so:
2S = 5100
Divide both sides by 2:
S = 2550.
The other way:
Or, you could use the formula for the sum of an arithmetic
series:
Edwin
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