Question

Sample response: 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. what did you include in your response? check all that apply. there is a common ratio between bounce heights. multiply 12 by 2/3. the height on the fourth bounce is 8 feet.

Answer 1

Explanation:

A Geometric sequence can be used:

To Model this sequence you need to use this formula

A (subscript n) = Ar(n-1)

a = value of the first term

n = the # of the term you want to find (For example, if you want to find the term number 3, it is 12)

r = the common ratio, this is obtained by dividing the second term in the sequence by the first.

So the value of r is = 2/3 because 27 times 2/3 = 18 which is the second term

n = 4 since you want to find the 4th term in the sequence

Plug it in and the results are

4th term = 27(2/3)^(4-1) = 8

The answer is 8