Bot GPT 4-o mini To find the common ratio of a geometric sequence, you divide any term by the previous term.
Let's calculate the common ratio \( r \) using the first and second terms:
\[ r = \frac{\text{second term}}{\text{first term}} = \frac{1/2}{2} = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4} \]
Now let's check the ratio between the second and third terms:
\[ r = \frac{\text{third term}}{\text{second term}} = \frac{1/8}{1/2} = \frac{1/8}{1/2} = \frac{1}{8} \times \frac{2}{1} = \frac{2}{8} = \frac{1}{4} \]
And let's check the ratio between the third and fourth terms:
\[ r = \frac{\text{fourth term}}{\text{third term}} = \frac{1/32}{1/8} = \frac{1/32}{1/8} = \frac{1}{32} \times \frac{8}{1} = \frac{8}{32} = \frac{1}{4} \]
Since the common ratio is the same for all pairs of consecutive terms, we can conclude that the common ratio of the geometric sequence \( 2, 1/2, 1/8, 1/32 \) is
\[ \boxed{\frac{1}{4}}. \]
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