Which one of these is a geometric sequence?

1. 1,5,9,13 ...

2. 1/4,1/2,1,2,4 ...

3. 2,3,5,9,17 ...

4. 3,-15,-33,-51,-69 ...

A geometric sequence this characteristic: If you take every term (other than the first term) and divide it by the previous term, you will get a ratio that is constant (also known as the common ratio). Another way to see it is that in a geometric series, you get to the next term by multiplying by some common ratio.

Only 1/4,1/2,1,2,4 ... is a geometric sequence because you have to multiply by 2 to get to the next term. E. g., 1/4 * 2 = 1/2 and 1/2 * 2 = 1 and 1 * 2 = 2 and 2 * 2 = 4, etc.