Answer:
We have been given many sequences below:
The sequence is said to be geometric if there is same ratio between consecutive terms
[tex]\frac{a_n}{a_{n-1}}[/tex]
So we will check all the sequences one by one:
(1) [tex]\frac{-9}{-2.7}=\frac{10}{3}[/tex]
[tex]\frac{-30}{-9}=\frac{10}{3}[/tex]
[tex]\frac{-100}{-30}=\frac{10}{3}[/tex].
Hence, geometric
(2) [tex]\frac{2.5}{-1}=-2.5[/tex]
[tex]\frac{-6.25}{2.5}=-2.5[/tex]
[tex]\frac{15.625}{-6.25}=-2.5[/tex]
Hence, geometric.
(3) [tex]\frac{9.2}{9.1}=0.010[/tex]
[tex]\frac{9.3}{9.2}=0.010[/tex]
[tex]\frac{9.4}{9.3}=0.010[/tex]
Hence, geometric.
(4) [tex]\frac{0.8}{8}=0.1[/tex]
[tex]\frac{0.08}{0.8}=0.1[/tex]
[tex]\frac{0.008}{0.08}=0.1[/tex]
Hence, geometric.
(5) [tex]\frac{-4}{4}=-1[/tex]
[tex]\frac{-12}{-4}=3[/tex]
Ratio is not same hence, not geometric.
