Answer:
594?
Step-by-step explanation:
The wording leaves a little to be desired. What does that 32 actually mean?
I don't think it is asking us to add on the distance it has to travel to get a bounce of 32. We are starting with a bounce that is 32 high.
The second bounce is 9/10 of that height which turns out to be 28.8.
The third bounce is 9/10 of 28.8 which is 25.92, I think, and then it continues on.
So here are the Givens
Given
a = 32
r = 9/10
n = 25
Formula
Sum = a(1 - r^n) / (1 - r)
Solution
Sum = 32*(1 - (9/10)^25) / (1 - 9/10)
Sum = 32*(1 - 0.07179) / ( 1 - 9/10)
Sum = 32*(0.9282) / 0.1
Sum = 29.7 / 0.1
Sum = 297
But that number represents only the distance going up. You must also take the distance going down. You have to double this answer.
2*sum = 2 * 297
Sum' = 594
================
The wording is a real snake. We don't really know if we need to include some height that was a start. If we do, the answer is 594 + k where k is a constant yet to be determined. Usually k is part of the problem.
Or do we take a = 32 as the first drop? We can't tell from the wording.
