SOLUTION: a grocer makes a display of cans in which the top row has one can and each subsequent row has two more cans than row above above it. If the display has 100 cans, how many rows does

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Question 720991: a grocer makes a display of cans in which the top row has one can and each subsequent row has two more cans than row above above it. If the display has 100 cans, how many rows does it contain?
Answer by fcabanski(1391) About Me  (Show Source):
You can put this solution on YOUR website!
This is an arithmetic sequence with a(0) (the first term) of 1, and a difference of 2.


In such a sequence the nth term (for this problem it's the number of rows) a(n) = a(0) + (n-1)d where d is the difference (2).


The 10th term, for example, is 1+9*2 = 19.


The sum of the first n terms S(n) = n*(a(0)+a(n))/2


Try that 10th term to see if the sum (the number of cans) is 100, or more than 100 (then try a smaller n) or less than 100 (then try a bigger n).


S(10) = 10*(1+19)/2 = 200/2 = 100.


When there are 10 rows there are 100 cans.

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