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Math Help - Geometric sequence

  1. #1
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    Unhappy Geometric sequence

    I am stuck on what to do here.. The answer is +- 1/8

    Q) Given that the first term of a geometric sequence is 4, and the third is 1, find possible values for the 6th term.

    Do you have to bring in logs or something?

    Thanks
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  2. #2
    Behold, the power of SARDINES!
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    Quote Originally Posted by Danielisew View Post
    I am stuck on what to do here.. The answer is +- 1/8

    Q) Given that the first term of a geometric sequence is 4, and the third is 1, find possible values for the 6th term.

    Do you have to bring in logs or something?

    Thanks
    a_n=ar^{n-1}

    so

    a_1=ar^{0} \iff 4=a

    now

    a_3=4r^2 \iff \frac{1}{4}=r^2 \iff \pm \frac{1}{2}=r

    Finally we get

    a_n=4(\pm \frac{1}{2})^{n-1}

    a_6=4(\pm \frac{1}{2})^5= \pm \frac{1}{8}
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