Question

12. Which one of the following is a geometric sequence?

A. −7, 10, 23, 36, . . .
B. 8, 4, 2, 1, 1/2, 1/4, . . .
C. 2, −3, 9/2, −18/4
D. 0, 1, 2, 3, . . .

Answer 1

Hi, the answer to this question is B.

Answer 2

B. 8, 4, 2, 1, 1/2, 1/4, . . .

Explanation:

A geometric sequence or geometric progression is a sequence where each term after the first one can be found by multiplying a certain factor.

So, basically, to find the geometric sequence, we just need to divide the second term by the first term and observe if it results a constant factor.

By doing that, we observe that the second equence is a geometric sequence with a reasonf of 1/2, let's demonstrate it

`8* (1)/(2)= 4 (second \ term)\\4 * (1)/(2)=2 (third \ term)\\ 2 * (1)/(2)= 1 (fourth \ term)\\ 1 * (1)/(2)= (1)/(2) (fiftg \ term)\\ (1)/(2) * (1)/(2)= (1)/(4) (sixth \ term)`

As you can observe, we perfectly built the sequence is its ratio or factor.

Therefore, choice B is a geometric sequence.