A ball is dropped from a height of 20 feet. Each time the ball bounces it returns to 7/9 of the height

Question

A ball is dropped from a height of 20 feet. Each time the ball bounces it returns to 7/9 of the height it fell from. Let an represent the maximum height of the ball on the nth bounce.

A) Find a formula that describes an. Express the common ratio as a fraction. Hint: Use an = a1r^n-1 and place r in parentheses!

an = _____________

B) What is the maximum height of the ball on the 6th bounce? Round your answer to three decimal places.

_______________ feet

Answer 1

a(n) = 20(7/9)^(n-1)

a(6) = 20(7/9)^5

a(6) = 20(.28463)

a(6) = 5.693 feet