To find the common ratio of a geometric sequence, you can divide any term by the previous term. Let's calculate it for the given geometric sequence: 2, 12, 18, 132.
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First, calculate the ratio between the second and first term: \[ \text{Common ratio} = \frac{12}{2} = 6 \]
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Next, calculate the ratio between the third and second term: \[ \text{Common ratio} = \frac{18}{12} = 1.5 \]
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Lastly, calculate the ratio between the fourth and third term: \[ \text{Common ratio} = \frac{132}{18} \approx 7.33 \]
Since the ratios are not consistent across the terms, this sequence is not a geometric sequence with a common ratio.
None of the provided responses (4, 12, Start Fraction 1 over 2 End Fraction, 14, Start Fraction 1 over 4 End Fraction, −1.5) correspond to a valid common ratio for this sequence as it does not maintain a consistent ratio throughout.
Thus, it appears that the sequence provided does not reliably follow a geometric sequence pattern. Please check the terms given for any possible errors or inconsistencies.