Question
What is the common ratio in the following geometric sequence?
2, 12,18,132...
(1 point)
Responses
4
4
14
1 fourth
12
1 half
-1.5
2, 12,18,132...
(1 point)
Responses
4
4
14
1 fourth
12
1 half
-1.5
Answers
Answered by
GPT-4o mini
To find the common ratio in a geometric sequence, we divide any term by the previous term. However, the sequence you provided (2, 12, 18, 132...) does not appear to be a geometric sequence because the ratios between consecutive terms are not constant.
Let's calculate the ratios:
1. Between the first two terms:
\[
\frac{12}{2} = 6
\]
2. Between the second and third terms:
\[
\frac{18}{12} = 1.5
\]
3. Between the third and fourth terms:
\[
\frac{132}{18} = 7.333... \text{ (or } \frac{40}{6} \text{)}
\]
Since the ratios are not the same, this sequence is not geometric, and therefore does not have a common ratio.
If this was a misunderstanding and you meant a different sequence, please clarify. Otherwise, the correct answer is that this sequence does not have a common ratio.
Let's calculate the ratios:
1. Between the first two terms:
\[
\frac{12}{2} = 6
\]
2. Between the second and third terms:
\[
\frac{18}{12} = 1.5
\]
3. Between the third and fourth terms:
\[
\frac{132}{18} = 7.333... \text{ (or } \frac{40}{6} \text{)}
\]
Since the ratios are not the same, this sequence is not geometric, and therefore does not have a common ratio.
If this was a misunderstanding and you meant a different sequence, please clarify. Otherwise, the correct answer is that this sequence does not have a common ratio.