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.

Answer 1

Hey there!

A= value of the first term
n= the number of the term you want to find
r= common ratio
 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 results are
4th term = 27(2/3)^(4-1)  = 8
The answer is 8


Hope this helps!

Answer 2

A sequence can be used to illustrate the difference in heights of each jump and develop a pattern from them. In this case, we have 27, 18, 12,... Assuming the pattern continues, we have the previous height divided by 3 and then subtracted from itself:
$a_n=a_{n-1}-\frac{a_{n-1}}{3}$

Here:
$a_4=a_3-\frac{a_3}{3}=12-\frac{12}{3}=12-4=8$