A ball is dropped to the ground from a height of 100 meters. It rebounds to a height of 50 meters after that first bounce and 25 meters after the second bounce. How high will it rebound on the seventh bounce?

0.78125 m

Step-by-step explanation:

First term of this geometric series is 50 m, and the common ratio is 1/2.

Thus, a (n) = (50 m) (1/2) ^ (n-1)

After the 7th bounce, the ball will reach a height of a (7) = (50 m) (1/2) ^ (7 - 1), or

a (7) = 50 / (2^6) m = 0.78125 m