What is the common ratio in the following geometric sequence?
2, 12
1
2
, 18
1
8
, 132
1
32
, . . .
(1 point)
Responses
14
1
4
Start Fraction 1 over 4 End Fraction
4
4
12
1
2
Start Fraction 1 over 2 End Fraction
−1.5
−
1.5
negative 1.5
2, 12
1
2
, 18
1
8
, 132
1
32
, . . .
(1 point)
Responses
14
1
4
Start Fraction 1 over 4 End Fraction
4
4
12
1
2
Start Fraction 1 over 2 End Fraction
−1.5
−
1.5
negative 1.5
Answers
Answered by
GPT-4o mini
To find the common ratio of a geometric sequence, you can divide any term by the term that precedes it. Let's calculate the common ratio using the first two terms of the sequence provided:
1. The first term is \( 2 \).
2. The second term is \( 12 \).
Now, we divide the second term by the first term:
\[
\text{Common Ratio} = \frac{\text{Second Term}}{\text{First Term}} = \frac{12}{2} = 6
\]
Next, let's check the next pairs of terms in the sequence:
- Third term: \( \frac{18}{12} = 1.5 \)
- Fourth term: \( \frac{132}{18} = 7.33 \)
It seems that this does not maintain a consistent common ratio. Let's check the terms again or see if there's an oversight.
If you meant to check the common ratio between \( 2 \) and \( 12 \), the correct common ratio found is \( 6 \), based on the provided terms. However, if there was a further intended sequence, let’s clarify that as needed.
Based on the original options you provided and the overview of what we calculated, there seems to be a confusion about the terms. Please confirm the sequence or check if it was a typo to resolve this. Based on my calculations:
\[
\text{Common Ratio} = 6
\]
Nonetheless, from the options listed, it appears none match \( 6 \).
If you need further clarification or calculations, feel free to ask!
1. The first term is \( 2 \).
2. The second term is \( 12 \).
Now, we divide the second term by the first term:
\[
\text{Common Ratio} = \frac{\text{Second Term}}{\text{First Term}} = \frac{12}{2} = 6
\]
Next, let's check the next pairs of terms in the sequence:
- Third term: \( \frac{18}{12} = 1.5 \)
- Fourth term: \( \frac{132}{18} = 7.33 \)
It seems that this does not maintain a consistent common ratio. Let's check the terms again or see if there's an oversight.
If you meant to check the common ratio between \( 2 \) and \( 12 \), the correct common ratio found is \( 6 \), based on the provided terms. However, if there was a further intended sequence, let’s clarify that as needed.
Based on the original options you provided and the overview of what we calculated, there seems to be a confusion about the terms. Please confirm the sequence or check if it was a typo to resolve this. Based on my calculations:
\[
\text{Common Ratio} = 6
\]
Nonetheless, from the options listed, it appears none match \( 6 \).
If you need further clarification or calculations, feel free to ask!