Question

find the common ratio of the geometric sequence -10, 20, -40, ...

Explanation:

Step1: Recall common ratio formula

The common ratio $r$ of a geometric sequence is $\frac{\text{any term}}{\text{previous term}}$.

Step2: Calculate using first two terms

$$r = \frac{20}{-10}$$

Step3: Simplify the expression

$$r = -2$$
(Verify with next pair: $\frac{-40}{20} = -2$, confirms consistency)

Answer:

$-2$