Represent the distance bounced by the ball in successive bounces by means of a sequence

Question

During each successive bounce,a tennis ball covers 80℅ of the horizontal distance it covered during the preceding bounce.The first bounce covered 2m.

Answer 1

The sum of the geometric series (distance bounced) is given by 2+0.8*2+0.8^2 *2+0.8^3 *2 +...=

2(1+0.8+0.8^2+0.8^3+...)=2(1-0.8^n)/(1-0.8) = 10(1-0.8^n), where n is the nth term.

When n=1 (first bounce), distance=10(0.2)=2m.

When n gets very large 0.8^n approaches 0 and the sum=10m.