Is the sequence -24,23,-22 a geometric sequence?

No. Geometric sequences have the same ratio between each successive pair of terms and $\frac{- 22}{23} \ne \frac{23}{-} 24$
Geometric sequences can always be expressed as ${a}_{i} = {a}_{1} {r}^{n - 1}$ where ${a}_{1}$ is the first term in the sequence and $r$ is a non-zero constant ratio between terms.