Question

What is the common ratio in the following geometric sequence?

2, 12, 18, 132,...
(1 point)
Responses

12
1 half

4
4

-1.5
-1.5

14

Answer 1

To find the common ratio in a geometric sequence, you can divide any term by the previous term.

Let's check the ratio between the consecutive terms:

1. From the first term (2) to the second term (12):
\[
\text{Common Ratio} = \frac{12}{2} = 6
\]

2. From the second term (12) to the third term (18):
\[
\text{Common Ratio} = \frac{18}{12} = 1.5
\]

3. From the third term (18) to the fourth term (132):
\[
\text{Common Ratio} = \frac{132}{18} = 7.33 (approximately)
\]

Since the common ratio is not consistent between the terms, this sequence does not form a geometric sequence.

Therefore, none of the provided responses (12, 1/2, 4, -1.5, and 14) are correct, as the common ratio is not constant.