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Math Help - Arithmetic Sequence.

  1. #1
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    Arithmetic Sequence.

    A super ball is dropped from a height of 64 feet. Each time it hits the ground, it rebounds 78% of the distance it has fallen. In theory how far will the ball travel before coming to rest? Explain your method and reasoning.

    so Ive tried a couple of equations/functions/ways to get this and it doesnt seem to be working. Can someone explain to me, how to start off? What to think about?

    And then how to get the answer?

    Thanks.
    Last edited by mr fantastic; May 19th 2010 at 07:33 PM. Reason: Restored deleted question.
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  2. #2
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    Quote Originally Posted by foreverbrokenpromises View Post
    A super ball is dropped from a height of 64 feet. Each time it hits the ground, it rebounds 78% of the distance it has fallen. In theory how far will the ball travel before coming to rest? Explain your method and reasoning.

    so Ive tried a couple of equations/functions/ways to get this and it doesnt seem to be working. Can someone explain to me, how to start off? What to think about?

    And then how to get the answer?

    Thanks.
    Lets think what is happening.

    t=0; h=64
    t=1; h=64*.78
    t=2; h=64*.78*.78=64*.78^2
    ....

    64\sum_{t=0}^{\infty}\left(\frac{39}{50}\right)^t

    This is a geometric series which can be solved:
    a\sum_{n=0}^{\infty}\left(\frac{p}{q}\right)^n=\fr  ac{a}{1-\frac{p}{q}} and \frac{p}{q}<1
    Last edited by dwsmith; May 18th 2010 at 08:42 PM.
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