SOLUTION: A ball dropped from a height of 12 m and rebounds one half the distance on each bounce. What is the total distance it travels?

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Question 1152042: A ball dropped from a height of 12 m and rebounds one half the distance on each bounce. What is the total distance it travels?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Ball drops 12m in the first step.
It rebounds 6m and drops back 6m covering 12m in the second step.
It rebounds 3m and drops back 3m covering 6m in the third step.
This continues indefinitely.
Mathematically :
S+=+12+%2B+12+%2B+6+%2B+3+...infinity
= 12++ (12+%2B+6+%2B+3 +...infinity)

Now (12+%2B+6+%2B+3 +...infinity) is an infinite GP with a+=+12 and r+=+1%2F2

=> S+=+12+%2B+%2812%2F%281+-+1%2F2%29%29
=> S+=+12+%2B+%2812%2F%281%2F2%29%29
=> S+=+12+%2B+24%29
=> S+=+36m