Which of the following sequences are geometric?
check all that apply.
a. 6, 18, 54, 162, 486
b. 2, 3, 5, 8, 13, 21
c. 2, 5, 8, 11, 14, 17
d. -4, -2, -1, -0.5, -0.25, -0.125

Let's start by first remembering what a "geometric sequence" is. A geometric sequence is a sequence of numbers that multiply by the same number each time. For example,
2, 4, 8, 16
is a geometric sequence since each number is multiplied by 2 from one to the next, but
2, 4, 6, 8 
is NOT a geometric sequence. We are adding 2 each time, but not multiplying, so it doesn't count. We have to be multiplying to have a geometric sequence.

[A] Let's look at A, are we multiplying by the same thing? 
6*3 = 18
18*3 = 54
54*3 = 162
162*3 = 486
Yes! We are multiplying by 3 each time. This is a geometric sequence!

[B] Are we multiplying by the same thing?
2*3/2 = 3
3*3/2 = 9/2 which is not 5.
NOPE

[C] Are we multiplying by the same thing?
2*5/2 = 5
5*5/2 = 25/2 which is not 8
NOPE

[D] Are we multiplying by the same thing?
-4*1/2 = -2
-2*1/2 = -1
-1*1/2 = -0.5
-0.5*1/2 = -0.25
-0.25*1/2 = -0.125
Yep, we are multiplying by 1/2 each time! This is a geometric sequence!