Finding sum in geometric series/sequence word problem

Question

A ball is dropped from a height of 5m. After each bounce the ball rises to 70% of its previous height. What is the total vertical distance that the ball travels (up and down) before it comes to a rest?

Detailed explanation appreciated

Answer 1

Draw and label a diagram!!!

The first drop is 5cm.

The first bounce is 2(0.7)(5) or 7

The second bounce is (0.7)(7) or 4.9

So the infinite geometric series is 7, 4.9, 3.43,

Determine the sum of the infinite series and add 5.