SOLUTION: Find an explicit rule for the nth term of a geometric sequence where the second and fifth terms are 36 and 2304, respectively.

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Find an explicit rule for the nth term of a geometric sequence where the second and fifth terms are 36 and 2304, respectively.       Log On


   

Question 1038314: Find an explicit rule for the nth term of a
geometric sequence where the second and fifth
terms are 36 and 2304, respectively.
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!

Geometric sequence:

__, 36, __, __, 2304, __, __, __, ...

The next term after 36 is 36r.  The term just after that is
36r² and then the fifth term 36r³ = 2304 

__, 36, 36r, 36r², 36r³ = 2304, __, __, __, ...

36r³ = 2304
r³ = 64
 r = 4

The second term is 36 so the first term is 36%2F4 or 9.

General term formula

a%5Bn%5D+=+a%5B1%5Dr%5E%28n-1%29

substitute first term a1 = 9, common ratio r = 4

a%5Bn%5D+=+9%2A4%5E%28n-1%29

Edwin