Question

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

Answer 1

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..