Question

Which sequences are geometric? Check all that apply.

A) –2.7, –9, –30, –100, ...
B) –1, 2.5, –6.25, 15.625, ...
C) 9.1, 9.2, 9.3, 9.4, ...
D) 8, 0.8, 0.08, 0.008, ...
F) 4, –4, –12, –20, ...

Answer 1

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.