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.

Question

Quizplus · Accepted Answer

The series is 6 + 2(6)(2/5) + 2(6)(2/5)^2 + ..., which is an infinite geometric series with first term a = 2(6)(2/5) and common ratio r = 2/5. The sum of the series is 6 + a/(1-r) = 6 + 12/3 = 14 ft.

Solve the Problem 25\frac { 2 } { 5 }52​ Of Its Height

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