# How do you find the 10th term in the geometric sequence 2,6,18,54,162,...?

##### 1 Answer

Mar 6, 2016

39,366.

#### Explanation:

Defining the sequence as {Sn}, n=1,2,3,...Sn+1/Sn = 3.

Sn+1 - 3 Sn = 0.

The obvious solution is Sn = 2X

S10 = 2X

The general solution of the difference equation

Sn+1 - a Sn = 0 is

Sn = CX

C is determined from the first value S1..