Question

What is the common ratio in the following geometric sequence? 2, 12,18,132...2, 12,18,132... (1 point) Responses 14141 fourth 4 4 12121 half -1.5

Answer 1

To find the common ratio of a geometric sequence, you divide any term by the previous term. In the sequence you provided: 2, 12, 18, 132, let's calculate the ratios.

1. From 2 to 12:
\[
\text{Common ratio} = \frac{12}{2} = 6
\]

2. From 12 to 18:
\[
\text{Common ratio} = \frac{18}{12} = 1.5
\]

3. From 18 to 132:
\[
\text{Common ratio} = \frac{132}{18} = 7.33 \text{ (or } \frac{22}{3} \text{)}
\]

The ratios between the terms are not constant, which means this is not a geometric sequence. The terms appear to have different ratios. Therefore, a common ratio does not exist for this sequence.

Based on your responses, none of them are correct as they imply the presence of a constant common ratio in a geometric sequence. If you still want to identify a different property of the sequence or clarify its nature, please provide additional details!