For each sequence, determine whether it appears to be geometric. If it does, find the common ratio. \begin{tabular}{|l|l|} \hline (a) $12,9,6,3, \ldots$ & O Geometric \\ & Common ratio: $r=\square$ \\ \hline (b) $-2,-8,-32,-128, \ldots$ & Not geometric \\ \hline & Common ratio: $r=\square$ \\ \hline (c) $400,200,100,50, \ldots$ & Not geometric \\ \hline & Common ratio: $r=\square$ \\ \hline \end{tabular}

Step 1 ：The sequence is \(12,9,6,3, \ldots\)

Step 2 ：To determine if a sequence is geometric, we need to check if the ratio between consecutive terms is constant.

Step 3 ：The ratio between the second and the first term is \(\frac{9}{12} = 0.75\)

Step 4 ：The ratio between the third and the second term is \(\frac{6}{9} = 0.67\)

Step 5 ：Since the ratios are not the same, the sequence is not geometric.

Step 6 ：\(\boxed{\text{Not geometric}}\)

Step 7 ：The sequence is \(-2,-8,-32,-128, \ldots\)

Step 8 ：The ratio between the second and the first term is \(\frac{-8}{-2} = 4\)

Step 9 ：The ratio between the third and the second term is \(\frac{-32}{-8} = 4\)

Step 10 ：Since the ratios are the same, the sequence is geometric and the common ratio is \(r = 4\)

Step 11 ：\(\boxed{\text{Geometric, } r = 4}\)

Step 12 ：The sequence is \(400,200,100,50, \ldots\)

Step 13 ：The ratio between the second and the first term is \(\frac{200}{400} = 0.5\)

Step 14 ：The ratio between the third and the second term is \(\frac{100}{200} = 0.5\)

Step 15 ：Since the ratios are the same, the sequence is geometric and the common ratio is \(r = 0.5\)

Step 16 ：\(\boxed{\text{Geometric, } r = 0.5}\)