Erms. For 3, 9, 27, ... the common ratio is 3 because: 3 X 3 = 9 9 X 3 = 27 So to find the 7th term you can do it two ways: One way: 3 is the 1st term, 9 is the 2nd term, 27 is the 3rd term so then 4th term: 27 X 3 = 81 5th term: 81 X 3 = 243 6th term: 243 X 3 = 729 7th term: 729 X 3 = 2,187 Another way: You can use the explicit formula a n = a 1 ⋅ r n − 1 , where a n is the nth term, a 1 is the first term, n is the number of the term, and r is the common ratio so a 7 = 3 ⋅ 3 7 − 1
a 7 = 3 ⋅ 3 6
a 7 = 3 ⋅ 729
a 7 = 2 , 187
Both ways get you to the same answer that the 7th term in that geometric sequence is 2, 187 .
Since there are 60 seconds in one minute, we can form the equation: From here, we can cross multiply. The train would travel 10,800 feet in one minute.
