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

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

You have everything here that you need.

a_n = a₁*r^n-1 , this is your hint.

a_n = nth term ( so if you are looking for the 7th term, then n = 7)

a₁ = 1st term ( what is the first height?)

r = common ratio (7/9)

n = depending on which term you are looking for.

Substitute.