A basketball is dropped from an original height of 9 feet and on each bounce, bounces up 2/3 the distance it fell. How far will it have traveled by the time it hits the ground the 4th time?

Question

anonymous · Answer

$$9+2\times 9\times \frac{2}{3}+2\times 9\times (\frac{2}{3})^2+2\times 9\times( \frac{2}{3})^3$$

anonymous · Answer

that is 
down 9 , the up and down, up and down, up and down
hence the 2 in the three terms

anonymous · Answer

a better question is how far does the ball bounce all together, but since it was not asked, no worries

anonymous · Answer

what would the final answer be?

anonymous · Answer

@satellite73

anonymous · Answer

is 103/3 correct?

anonymous · Answer

well thats what i got for the answer to the long answer you gave me, but i'm not sure how to find the solution to the problem

nottim · Answer

hey @satellite73 isn't there a better formula for this situation?

anonymous · Answer

@NotTim if so can you explain it to me?

nottim · Answer

eh...im a forgetter. can remember.

nottim · Answer

but I think what you think is correct. go with it.

anonymous · Answer

i still don't understand how to find the final answer from that