Posted by Vivian on Wednesday, March 14, 2012 at 8:14am.
Mia is stacking copies of a new book in a squarepyramid display by the front window of her bookstore. for each consecutive layer, she places one book where four meet.
A. I the bottom row of the display has 144 books and there is one book on the top, determine how many rows of books are in her pyramid.
B. Explain how to find the total number of books in the display.
C. If she removes the top four rows, how many books are left in the pyramid display?

math  Reiny, Wednesday, March 14, 2012 at 8:34am
You might want to make a sketch to show that the bottom level is a 12 by 12 square
the second level is a 11 by 11 square, etc
So your sum is 12^2 + 11^2 + 10^2 + ... 2^2 + 1^2
you could just add up these numbers to get 650
or you could use a formula that says
the sum of squares of consecutive numbers from 1 to n is
n(n+1)(2n+1)/6 which gives us 650
for the last part, find the sum of books removed at the top and subtract that from 650
btw, did you realize that the books would have to be square in shape?
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