Question

What is the common ratio of the sequence below?
2/3, 1/6, 1/24, 1/96....
A 1/9
B 1/4
C 4
D 9

Answer 1

To find the common ratio of the sequence \( \frac{2}{3}, \frac{1}{6}, \frac{1}{24}, \frac{1}{96} \), we can divide any term by the previous term.

Let's calculate the common ratio \( r \):

1. From the first term \( \frac{2}{3} \) to the second term \( \frac{1}{6} \):
\[
r = \frac{\frac{1}{6}}{\frac{2}{3}} = \frac{1}{6} \times \frac{3}{2} = \frac{3}{12} = \frac{1}{4}
\]

2. Now, let's check from the second term \( \frac{1}{6} \) to the third term \( \frac{1}{24} \):
\[
r = \frac{\frac{1}{24}}{\frac{1}{6}} = \frac{1}{24} \times 6 = \frac{6}{24} = \frac{1}{4}
\]

3. Lastly, let's check from the third term \( \frac{1}{24} \) to the fourth term \( \frac{1}{96} \):
\[
r = \frac{\frac{1}{96}}{\frac{1}{24}} = \frac{1}{96} \times 24 = \frac{24}{96} = \frac{1}{4}
\]

Since in each case we found that the common ratio \( r = \frac{1}{4} \), the answer is:

**B) \( \frac{1}{4} \)**