Find indicated term of the geometric sequence

Question

a1=6,a4=1, 9th term

Answer 1

C(r^0) = 6

C = 6

 

The geometric series is now 6*r^(n-1), n=1,2,3,4,5,...,infinity

 

The 4th term is 1. So,

  For n=4,    1 = 6*r^(4-1)

 

                   1/6 = r^3

 

                   r=cube-root(1/6) = (1/6)^(1/3)

 

The geometric sequence is   6*[(1/6)^(1/3)]^n-1 = 6 * cube-root(1/6)^(n-1)/3, n=1,2,3,4,... infinity

 

First term: 1

2nd term:  6*(1/6)^(1/3)

3rd term: 6* (1/6)^(2/3)

4th term: 6 * (1/6) = 1

5th term = 6*(1/6)^(4/3)

6th term = 6*(1/6)^(5/3)

7th term = 6(1/6)^2 = 6/36 = 1/6

8th term = 6(1/6)^(7/3)

9th term = 6(1/6)^(8/3)

10th term = 6(1/6)^3 = 6/216 = 1/36