Which one of the following is a geometric sequence?

a.2,-3,9/2,-18/4
b.-7,10,23,36
c.0,1,2,3
d.8,4,2,1,1/2,1/4

Explanation:

Each term of sequence D has us multiply by 1/2, or divide by 2, to get the next term.

8 * (1/2) = 4

4 * (1/2) = 2

2 * (1/2) = 1

1 * (1/2) = 1/2

(1/2) * (1/2) = 1/4

and so on

We can divide any term, except the first term, by its prior term to get the common ratio, so for instance,

common ratio = (term2)/(term1) = 4/8 = 1/2

and if we apply this to all possible pairs of consecutive terms then we see that we get 1/2 across the board. This confirms we have a geometric sequence.

The other sequences do not fit this pattern.

For example, choice B has

(term2)/(term1) = 10/(-7) = -1.43

and

(term3)/(term2) = 23/10 = 2.30

those results are not the same; therefore, sequence B is not geometric. The other answer choices can be ruled out in a similar fasion.

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