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Thread: 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 $\displaystyle t_n = ar^{n-1}$.

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

    This means $\displaystyle 440r^{11} = 880$

    $\displaystyle r^{11} = 2$

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


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


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

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

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

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