PROBLEM:A BALL WAS DROPS 27 INCHES AFTER THE FIRST SECOND AND THIRD BOUNCE THE HEIGHTS WERE 18 12 AND 8 hOW MANY DID IT TAKE TO GET TO 3 INCHES

Answer 1

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

Tn = 27 (2/3)^n

So, solve for n in

27 (2/3)^n = 3
(2/3)^n = 3/27 = 1/9
n = log_2/3(1/9) = 5.4

Looks like no particular hop is 3 inches. Let's extend the sequence:

27 18 12 8 16/3 32/9 64/27

As we calculated, the 6th hop is the soonest the height is below 3 inches.