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Math Help - help on garde 11 geometric sequence and series problem

  1. #1
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    help on garde 11 geometric sequence and series problem

    the question is:

    A ball is dropped from a height of 8m. it rebounds to 3/4 of its height after each bounce. Find the total distance travelled by the ball when it touches the floor on the tenth bounce.



    this is my solution


    first bounce: 8
    up 6 down 6 making 12 added at second bounce touch
    next up and down 4.5 each making 9 added at 3rd bounce touch

    Disregarding first bounce, the first term is 12 and r = 3/4 and n will equal 9

    so that's 12 (1 - (3/4)^9) over (1 - 3/4) = 44.396, plus 8 = 52.396 m

    See what you think
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  2. #2
    Senior Member eumyang's Avatar
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    Looks fine to me.
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  3. #3
    MHF Contributor
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    Looks kinda fine to me too; but I'm not sure what "a bounce" is;
    like, is the 1st bounce 8 down and 6 up?
    If they mean 1st bounce is 6 up and 6 down, then you have to
    go to ^10, which will end up at 53.297 ... what you think?!
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