To find the common ratio in a geometric sequence, you can take the second term and divide it by the first term. The common ratio \( r \) can also be found by dividing any term by its preceding term.
For the given sequence:
- The first term \( a_1 = 2 \)
- The second term \( a_2 = \frac{1}{2} \)
Calculating the common ratio \( r \):
\[ r = \frac{a_2}{a_1} = \frac{\frac{1}{2}}{2} = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4} \]
We can also check with the next terms:
- The third term \( a_3 = \frac{1}{8} \)
\[ r = \frac{a_3}{a_2} = \frac{\frac{1}{8}}{\frac{1}{2}} = \frac{1}{8} \times \frac{2}{1} = \frac{1}{4} \]
- The fourth term \( a_4 = \frac{1}{32} \)
\[ r = \frac{a_4}{a_3} = \frac{\frac{1}{32}}{\frac{1}{8}} = \frac{1}{32} \times \frac{8}{1} = \frac{1}{4} \]
In all cases, the common ratio is consistent. Thus, the common ratio in the geometric sequence is:
\(\frac{1}{4}\)
The correct response is:
Start Fraction 1 over 4 End Fraction (or \(\frac{1}{4}\))