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Thread: generalizing pictorial growth pattern

  1. December 13th 2009, 03:45 PM #1
    ElenaS519
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    generalizing pictorial growth pattern

    This problem is for my algebra for elementary teachers class and I am stumped!
    See attachment
    I am looking for an explicit formula
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    Last edited by ElenaS519; December 13th 2009 at 05:01 PM.
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  2. December 13th 2009, 04:49 PM #2
    Gusbob
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    One line of triangles takes 3 toothpicks
    Two lines of triangles takes 9 toothpicks
    Three three lines of triangles takes 18 toothpicks

    How many toothpicks does it take to make 4? Can you find a pattern?

    Hint: The differences between the terms form an arithmetic series

    Spoiler:

    # of toothpicks = \frac{3n(n+1)}{2} where n is the number of lines of triangles

    Last edited by Gusbob; December 13th 2009 at 05:39 PM.
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  3. December 13th 2009, 06:34 PM #3
    ElenaS519
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    right, I got that, but I am looking for an EXPLICIT formula for the number of line segments needed for the nth figure.
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  4. December 13th 2009, 06:48 PM #4
    ElenaS519
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    oh ok...nevermind. Thank you so much!
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