math precalculus

Question

A hard rubber ball is dropped from a roof of a building that is 8 meters high. The ball rises to 45% of the height from the bounce. what is the total vertical distance that the ball has traveled just before it hits the floor the 6th time?

Answer 1

8 + S₆, where S₆ = 3.6(1 - 0.45⁶) / (1 - 0.45)

Answer 2

Total vertical distance D = 8 + 2(0.45 ·8 + 0.45²·8 +... + 0.45⁵·8)= 8 + 16(0.45 + 0.45² + ...+ 0.45⁵) =

8 + 16·0.45(1 - 0.45⁵)/(1 - 045) = 20.849345.

We use formula for sum of 1st n terms of geometric series.