Question

A bouncing ball reaches a height of 27 feet at its first peak, 18 feet at its second peak, and 12 feet at its third peak. Describe how a sequence can be used to determine the height of the ball when it reaches its fourth peak.
Pleaaaase I need help!!

Answer 1

27*2/3=18
18*2/3=12

Answer 2

I would look at the ratio of two terms
and the difference of two terms
to see if there might be a pattern

for example, 27, 18, 12
the difference between 27 and 18 is 9
the difference between 18 and 12 is 6
That is not a constant difference.

Let's try ratios:
27/18 = 1.5
18/12 = 1.5
that looks promising... we get the same ratio
so on the next bounce, expect
18/x = 1.5

maybe it's easier if we flip the ratio 1.5 (3/2) to 2/3 and so
18= 2/3 * 27
12= 2/3* 18 = 2/3 * 2/3 * 27

If we try to make a pattern
first peak = (2/3)^0 * 27
2nd peak = (2/3)^1 *27
3rd peak = (2/3)^2 * 27

Answer 3

Thank you!!!