Question

A bouncing ball reaches a height of 27 feet at its first peak, 18 feet at its second peak, and 12 feet at its third peak. Describe how a sequence can be used to determine the height of the ball when it reaches its fourth peak.

Answer 1

There is a common ratio of 2/3 between the height of the ball at each bounce. So, the bounce heights form a geometric sequence: 27, 18, 12. Two-thirds of 12 is 8, so on the fourth bounce, the ball will reach a height of 8 feet.

Explanation:

Sample response :)

Answer 2

The sequence:
a 1 = 27 ft, a 2 = 18 ft, a 3 = 12 ft.
a 2 = a 1 * q
q = a 2 / a 1 = 18 / 27 = 2 / 3
a 4 = a 3 * q = 12 * 2 / 3 = 8 ft