Solve the Problem $$25 + \sum _ { \mathrm { k } = 1 } ^ { \mathrm { n } } 50 \left( 0.7 ^ { \mathrm { k } } \right) \text { feet. }$$

Essay

Solve the problem.
-A ball is dropped from a height of 25 feet. Each time it strikes the ground, it bounces up to 0.7 of the previous
height. The total distance the ball has travelled before the second bounce is 25 + 2(25 · 0.7) feet, and the total
distance the ball has travelled before bounce n + 1 is $$25 + \sum _ { \mathrm { k } = 1 } ^ { \mathrm { n } } 50 \left( 0.7 ^ { \mathrm { k } } \right) \text { feet. }$$ Use facts about infinite geometric series to calculate the total distance the ball has travelled by the time it has stopped
bouncing.