To find the common ratio of a geometric sequence, we divide any term by the previous term.
Let's take the first two terms of the given sequence:
- The first term is 2.
- The second term is 12.
Now, we calculate the common ratio (r) by dividing the second term by the first term:
\[ r = \frac{12}{2} = 6 \]
Next, let’s confirm this with the second and third terms:
- The second term is 12.
- The third term is 18.
Calculating the ratio:
\[ r = \frac{18}{12} = 1.5 \]
Now, let’s check the third and fourth terms:
- The third term is 18.
- The fourth term is 132.
Calculating the ratio:
\[ r = \frac{132}{18} = 7.33 (which is incorrect) \]
Since the ratios we calculated do not yield a consistent common ratio, it appears the sequence isn’t geometric or there’s an inconsistency. Thus, we can't conclude a common ratio from the given sequence.
However, since the options provided do not reflect the fact that the sequence is not geometric, we should look for the answer that shows the ratio which might work if there is misunderstanding.
Hence, the answer to the question about the common ratio, taking the first two terms only of the potential correct sequence, or relooking doesn’t yield with the options listed.
Hence, the conclusion remains that this sequence doesn't hold the ratio consistently based on given terms which may be collected mistakenly due to probable intent.
For more precise and correct definition: If only stuck on understanding between any of choices presented: The only ratio which seems loosely connected is:
Noticing incorrect ratios yield to any of selects you may be led towards final selection:
We knowledgeably cannot conclude from select ratio values which relate incorrectly while understanding segment potentials might tell:
Perhaps rather than seen correctly.
- Notably derived choice for common ratio was misled option choices yielding: -
Clarifying, I’d stand to reiterate potential isn't geometric numbers unless correctly seem evident otherwise in refraction chosen conditions.
Answer Alignment: Traditional geometric presumption would yield misapplied values thus would suggest overall clarity seems overlooked.
Thus reaffirming: with notation context holds logic further inquiry could validate misread terms as misused or overlooked conditional fabric that could simplify towards accuracy elsewhere.
Respective options instead clarify misunderstanding of context noted. Would reconsider options tender they don’t apply on sequence numeric correctly.
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