Gr.11 Math

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A large company has a phone tree to contact its employees in case of an emergency factory shutdown. Each of the five senior managers calls three eployees, who calls three other employees and so on. If the tree consists of seven levels, how many employees does the company have?

Could someone explain to me how to solve this? Which geometric formula would I have to use?

  • Gr.11 Math -

    THE first layer 5
    second layer 5x3
    third layer 5x3x3
    see the pattern?5*3^(n-1)
    where n is the layer.
    employees total is the sum of all of these. Looks like a geometric series..

  • Gr.11 Math -

    If you call the five senior managers as the first level, then in the second level there would be 15 and in the third level there would be 45

    so you want the 7th term in this sequence, not the sum of 7 terms (because you would be counting the same people again and again)

    so a=5, r=3, and t(7) = ar^6 = 5(3)^6 = 3645

    check my arithmetic.

  • Gr.11 Math -

    Use the formula

    Sn = a(r^n-1)
    --------
    r-1

  • Gr.11 Math -

    s7=5(3^7-1)/3-1
    =5465

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