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Math Help - Geometrical sequence word problem help..

  1. #1
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    Geometrical sequence word problem help..

    A beetle starts at a point O on the floor. It walks 1m east, then 1/2m west, then 1/4m east and so on. How far it finish off O and how far did it actually walk?

    Now here's my working:

    We are given, ratio r = -(1/2), and first term a = 1 ... Since |r| < 1, it's a series that converges to a limit, so:

    S = a / 1 - r
    S = 1 / 1 - (-1/2) = 2/3

    Therefore, the beetle ends up 2/3m from O.

    Now ... I want help with how far did it actually walk. How should I go about calculating that?
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  2. #2
    Member Greengoblin's Avatar
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    The total distance walked is given by the infinite series:

    d=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}\cdots

    since distance has no sense of direction, only magnitude. Does this help?
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  3. #3
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    Quote Originally Posted by Greengoblin View Post
    The total distance walked is given by the infinite series:

    d=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}\cdots

    since distance has no sense of direction, only magnitude. Does this help?
    Thanks but how to calculate how long this series continue until?
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  4. #4
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    Quote Originally Posted by struck View Post
    Thanks but how to calculate how long this series continue until?
    It's an infinite geometric series. S = \frac{a}{1 - r} where r = 1/2.
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