To find the common ratio in a geometric sequence, you divide any term by the previous term.
Let's use the first two terms of the sequence you provided:
- The first term \( a_1 = 2 \)
- The second term \( a_2 = 12 \)
The common ratio \( r \) can be calculated as follows:
\[ r = \frac{a_2}{a_1} = \frac{12}{2} = 6 \]
Now, checking the next term \( a_3 = 18 \) from \( a_2 = 12 \):
\[ r = \frac{a_3}{a_2} = \frac{18}{12} = 1.5 \]
This does not match the previous calculation, indicating that the sequence is not consistent and is not a geometric sequence.
So, let's verify:
Next, check between \( a_3 = 18 \) and \( a_4 = 132 \):
\[ r = \frac{a_4}{a_3} = \frac{132}{18} = 7.3333 \ldots \]
This also does not yield a consistent ratio with other terms. We see that the sequence does not maintain a single common ratio throughout.
Thus, the common ratio you provided in the answer choices does not apply since this is not a consistent geometric sequence. If you were looking to identify a specific term in another context, please clarify and we can explore that!