Understanding the Pattern

* First drop: 100 cm

* First bounce: 100 cm / 2 = 50 cm (up) + 50 cm (down) = 100 cm

* Second bounce: 50 cm / 2 = 25 cm (up) + 25 cm (down) = 50 cm

* Third bounce: 25 cm / 2 = 12.5 cm (up) + 12.5 cm (down) = 25 cm

And so on...

Calculating the Total Distance

This forms a geometric series where:

* The first term (a) is 100 cm

* The common ratio (r) is 1/2

The total distance is the sum of the infinite geometric series:

S = a / (1 - r)

S = 100 cm / (1 - 1/2)

S = 100 cm / (1/2)

S = 200 cm

Therefore, the ball will cover a total distance of 200 cm before coming to rest.