# How do you find the next three terms in the geometric sequence 4, -2, 1, -, ... ?

Nov 8, 2015

The common ratio of this sequence is $- \frac{1}{2}$, so the sequence goes:

$4 , - 2 , 1 , - \frac{1}{2} , \frac{1}{4} , - \frac{1}{8} , \ldots$

#### Explanation:

Geometric sequences have a fixed ratio between successive pairs of terms. in the case of this sequence, the common ratio is:

$\frac{- 2}{4} = - \frac{1}{2}$.

To find the next term in the sequence just multiply the previous term by the common ratio.

The general term of the sequence can be written:

${a}_{n} = {a}_{1} \cdot {r}^{n - 1}$

where ${a}_{1}$ is the first term and $r$ the common ratio.