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

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 ${3}^{n - 1}$.
S10 = 2X${3}^{9}$ = 39,366.
The general solution of the difference equation
Sn+1 - a Sn = 0 is
Sn = CX${a}^{n - 1}$
C is determined from the first value S1..