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Math Help - Geometric sequences

  1. #1
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    Geometric sequences

    im really stuck on this question.

    The sum of the first 4 terms ofa geometric series is 30, and the sum of the infinite series is 32. Find the first 3 terms.

    i know i have to find a and r, however Im not sure how to do it.
    Do i work out what a is for both sides??? HELP!!!.. PLEASE
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  2. #2
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    Re: Geometric sequences

    The sum of a series for the first n terms is a\frac{1-r^n}{1-r}

    The sum of an infinite geometric series (assuming |r|<1) is \frac{a}{1-r}

    With your information
    a\frac{1-r^4}{1-r}=30

    \frac{a}{1-r}=32


    Note that
    a\frac{1-r^4}{1-r}= \frac{a}{1-r}\cross (1-r^4)=30
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