# math

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A ball has a 75% rebound ratio. When you drop it from a height of 16 ft, it bounces and bounces...
When it strikes the ground for the second time, the ball has traveled a total of 28 ft in a downward direction. How far downward has the ball traveled when it strikes the ground for the 17th time?

• math -

T(1)=16
T(2)=12
T(3)=9
...
T(n)=16(3/4)^(n-1)
It is a geometric progression (GP) with a ratio of 3/4.

The sum to n terms of a GP is:
S(n)=16(1-(3/4)^n)/(1-(3/4))
Substitute n=17 in the above formula to get S(17), the total downward distance.

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