Geometric sequences are characterized by having a common ratio, r. It is calculated by getting the ratio of a(n+1) and a(n). We can determine which is the geometric sequence, if we calculate which sequence will have a common ratio. We do as follows:
A) –2.7, –9, –30, –100, ...
-9/-2.7=10/3
-30/-9=10/3
B) –1, 2.5, –6.25, 15.625, ...
2.5/-1=-2.5
-6.25/2.5=-2.5
C) 9.1, 9.2, 9.3, 9.4, ...
9.2/9.1=92/91
9.3/9.2=93/92
D) 8, 0.8, 0.08, 0.008, ...
0.8/8=1/10
0.08/0.8=1/10
F) 4, –4, –12, –20, ...
-4/4 = -1
-12/-4=3
Therefore, options A,B and D represents a geometric sequence.