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Math Help - Geometric progression

  1. #1
    Newbie parmis's Avatar
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    Geometric progression

    5 sentences makes Geometric progression. their multiplying is 243.
    how much is the multiplying first sentence and fifth sentence?
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  2. #2
    MHF Contributor ebaines's Avatar
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    Re: Geometric progression

    I think what you mean is this:

    Given that a geometric series of 5 terms multiplies to 243, what is the product of the first and fifth term?

    The product of 5 terms of a geometric series is  a \times ar \times ar^2 \times ar^3 \times ar^4= a^5r^{10} . The product of the 1st and 5th terms is a^2r^4, which is equal to (a^5r^{10})^{2/5}. Hence the product of the 1st and 5th terms is 243^{2/5}. Since 243 = 3^5, this becomes (3^5)^{2/5} = 3^2=9.
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