SOLUTION: A grocer makes a display of cans in which the top row has one can and each lower row has two more cans than the row above it. If the display contains 100 cans, how many rows does i
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Question 1064252: A grocer makes a display of cans in which the top row has one can and each lower row has two more cans than the row above it. If the display contains 100 cans, how many rows does it contain? Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! A grocer makes a display of cans in which the top row has one can and each lower row has two more cans than the row above it. If the display contains 100 cans, how many rows does it contain?
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Series:: 1+3+5+7+...
That is an arithmetic series with a(1) = 1 and d = 2
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Sum Formula:: S(n) = (n/2)(a(1)+a(n))
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Solve for "n"::
(n/2)(1+a(n)) = 100
But a(n) = a(1)+(n-1)*2
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n(1+1+2n-2) = 200
n*2n = 200
2n^2 = 200
Ans:: n = 10 rows
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Cheers,
Stan H.
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