# How do you find the next three terms in the geometric sequence 9, -3, 1, , ... ?

Apr 24, 2016

$- \frac{1}{3} , \frac{1}{9} , - \frac{1}{27}$

#### Explanation:

This is a GP series having first term $a = 9$
and common ratio $r = - \frac{3}{9} = - \frac{1}{3}$
So
multiplying 3rd term 1 by $- \frac{1}{3}$ we get 4th term $1 \times \left(- \frac{1}{3}\right) = - \frac{1}{3}$
multiplying 4th term $- \frac{1}{3}$by $- \frac{1}{3}$ we get 5th term $- \frac{1}{3} \times \left(- \frac{1}{3}\right) = \frac{1}{9}$
and similarly the 6th term $\frac{1}{9} \times \left(- \frac{1}{3}\right) = - \frac{1}{27}$