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A ball is dropped from a height of 4 feet, and each time it hits the ground it rebounds to ¾ of the previous height. What is the total distance that the ball will have traveled when it reaches the top of its twentieth rebound?

I know that I have to use the sum formula because I have to find the total distance bounced, but how would I do that? thanks

Alex
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  • Have you looked here http://math.stackexchange.com/questions/481991/bouncing-ball-geometric-sequence-question or here http://math.stackexchange.com/questions/481991/bouncing-ball-geometric-sequence-question or here http://math.stackexchange.com/questions/243840/superball-total-bounce-distance or here https://www.google.com/search?q=distance+traveled+by+bouncing+ball+stack+exchange – Jared Apr 06 '14 at 02:08

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Lets say it falls from x feet. It falls x feet and then starts a bounce of $\frac{3}{4}x$ The bounce after that is $(\frac{3}{4})^2x$ as it is 3/4 of the previous bounce. Each bounce after this raises $\frac{3}{4}$ to a higher power. Do you think you can find the sum now?

Asimov
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  • I think I have to multiply everything by two, then subtract 4 or get the sum of this sequence from the first bounce to the 20th bounce. That covers all distance traveled by the ball travelling up starting from after the first bounce and ending after the 20th. not 100% sure still more suggestions would be good.thanks – Alex Apr 06 '14 at 02:11
  • The first fall only happens once, so you subtract x from the final sum, and when it reaches the top of the 20th rebound it has only done half of the 20th bounce, so subtract $(\frac{3}{4})^{20} x$ from the total. That should be it – Asimov Apr 06 '14 at 21:37