Solve the Problem $$\frac { 2 } { 5 }$$ Of Its Height

Multiple Choice

Solve the problem.
-A ball drops from a height of 6 ft. With each bounce, the ball rebounds to $$\frac { 2 } { 5 }$$ of its height. The total vertical distanced traveled is given by $$6 + ( 2 ) ( 6 ) \left( \frac { 2 } { 5 } \right) + 2 ( 6 ) \left( \frac { 2 } { 5 } \right) ^ { 2 } + 2 ( 6 ) \left( \frac { 2 } { 5 } \right) ^ { 3 } \cdots$$ After the first term, the series is an infinite geometric series. Compute the total vertical distance traveled.

A) The total vertical distance traveled is 8 ft.
B) The total vertical distance traveled is 14 ft.
C) The total vertical distance traveled is 10 ft.
D) The total vertical distance traveled is 4 ft.