a golf ball is dropped onto concrete from 2 meters up. Each time it bounces, it rebounds to 2/3 of its previous height. On the sixth rebound, how much will it rise

Step-by-step explanation:

The ratio is the same each time (2/3), so this can be modeled as a geometric sequence.

an = a₁ (r) ^ (n-1)

where an is the nth term, a₁ is the first term, and r is the common ratio.

On the first rebound, the ball rises to 2/3 * 2 = 4/3, so a₁ = 4/3.

an = 4/3 (2/3) ^ (n-1)

On the sixth rebound, the ball rises to:

a₆ = 4/3 (2/3) ^ (6-1)

a₆ = 4/3 (32/243)

a₆ = 128/729

a₆ ≈ 0.176