Question

Which of the following is a geometric sequence?

Answer 1

Geometric sequences use either division or multiplication as the common ratio.  The third choice down has a common ratio of 3.  1*3=3, 3*3=9, 3*9=27, etc.

Answer 2

Answer:

Option C. is the geometric sequence.

Step-by-step explanation:

In a geometric sequence there should be a common ratio in each successive term.

Now we will check the common ratio in each option.

A). $1, \frac{1}{2}, \frac{1}{6}, \frac{1}{24}........$

In this sequence if we find the common ratio

Ratio of second and first term = $\frac{\text{Second term}}{\text{First term}}$

= $\frac{\frac{1}{2}}{1}=\frac{1}{2}$

Similarly ratio of third and second term = $\frac{\text{Third term}}{\text{Second term}}$

= $\frac{\frac{1}{6}}{\frac{1}{2}}$

= $\frac{2}{6}$

= $\frac{1}{3}$

Here ratios are not common. Therefore, sequence is not a geometric sequence.

B). -1, -1, 1, -1, -1..............

ratio of second and first term = $\frac{-1}{-1}=1$

ratio of third and second term = $\frac{1}{-1}=-1$

Ratios are not equal so sequence is not a geometric sequence.

C). 1, 3, 9, 27...............

ratio of second and first term = $\frac{3}{1}=3$

ratio of third and second term = $\frac{9}{3}=3$

Both the ratios are same therefore, sequence is geometric.

D). 3, 6, 9, 12..............

ratio of second and first term = $\frac{6}{3}=2$

ratio of third and second term = $\frac{9}{6}=\frac{3}{2}$

Ratios are not equal so sequence is not a geometric sequence.