For each sequence, determine whether it appears to be geometric. If it does, find the common ratio. Geometric (a) $4,2,1,-2, \ldots$ Common ratio: $r=$ Not geometric Geometric (b) $12,9,6,3, \ldots$ Common ratio: $r=$ Not geometric Geometric (c) $4,2,1, \frac{1}{2}, \ldots$ Common ratio: $r=$ Not geometric

Step 1 ：A sequence is geometric if the ratio of any two consecutive terms is constant. This ratio is called the common ratio. We can find the common ratio by dividing any term in the sequence by the preceding term.

Step 2 ：Let's calculate the ratio for each sequence and check if it's constant.

Step 3 ：For the first sequence $4,2,1,-2$, the ratios are $\frac{2}{4}=0.5$, $\frac{1}{2}=0.5$, and $\frac{-2}{1}=-2$. The ratios are not constant, so the sequence is not geometric.

Step 4 ：For the second sequence $12,9,6,3$, the ratios are $\frac{9}{12}=0.75$, $\frac{6}{9}=0.75$, and $\frac{3}{6}=0.5$. The ratios are constant, so the sequence is geometric with a common ratio of $r=0.75$.

Step 5 ：For the third sequence $4,2,1,0.5$, the ratios are $\frac{2}{4}=0.5$, $\frac{1}{2}=0.5$, and $\frac{0.5}{1}=0.5$. The ratios are constant, so the sequence is geometric with a common ratio of $r=0.5$.

Step 6 ：Final Answer: \(\boxed{(a) \text{ Not geometric}}\), \(\boxed{(b) \text{ Geometric with a common ratio of } r=0.75}\), \(\boxed{(c) \text{ Geometric with a common ratio of } r=0.5}\)