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math

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Mia is stacking copies of a new book in a square-pyramid 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 -

    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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