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Math Help - geometric series/sequence given question

  1. #1
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    geometric series/sequence given question

    consider the following geometric sequences and find the terms indicated:

    *The 1st term is 440 and the 12th is 880. find S6
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  2. #2
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    You should know that t_n = ar^{n-1}.

    So a = t_1 = 440 and t_{12} = ar^{11} = 880.

    This means 440r^{11} = 880

    r^{11} = 2

    r =2^{\frac{1}{11}}.


    This means t_n = 440(2^{\frac{1}{11}})^{n-1}.


    You should also know that S_n = \frac{a(r^n-1)}{r-1}

    So S_6 = \frac{440[(2^{\frac{1}{11}})^6-1]}{2^{\frac{1}{11}} - 1}

     = \frac{440(2^{\frac{6}{11}} - 1)}{2^{\frac{1}{11}} - 1}.

    Use a calculator to simplify.
    Last edited by Prove It; July 12th 2010 at 01:58 AM.
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