Complete the pattern.
`100, 50, 33 (1/3), 25,20`, ?

Options

A. 15
B. `16(1/3)`
C. `17(2/3)`
D. `16(2/3)`

Answer

To complete the given pattern: `100, 50, 33 (1/3), 25, 20`, we need to identify the underlying rule or pattern in the sequence.

### Step-by-Step Solution:

1. **Identify the first term**: The first term is 100.

2. **Observe the second term**: The second term is 50. We can express this as:
\[ 50 = \frac{100}{2} \]

3. **Observe the third term**: The third term is 33 (1/3). We can express this as:
\[ 33 \frac{1}{3} = \frac{100}{3} \]

4. **Observe the fourth term**: The fourth term is 25. We can express this as:
\[ 25 = \frac{100}{4} \]

5. **Observe the fifth term**: The fifth term is 20. We can express this as:
\[ 20 = \frac{100}{5} \]

6. **Identify the pattern**: We see that the terms can be expressed as:
- First term: \( \frac{100}{1} \)
- Second term: \( \frac{100}{2} \)
- Third term: \( \frac{100}{3} \)
- Fourth term: \( \frac{100}{4} \)
- Fifth term: \( \frac{100}{5} \)

This indicates that the nth term can be expressed as:
\[ \text{nth term} = \frac{100}{n} \]

7. **Find the sixth term**: To find the sixth term, we apply the same rule:
\[ \text{Sixth term} = \frac{100}{6} \]

8. **Calculate the sixth term**:
\[ \frac{100}{6} = 16 \frac{2}{3} \]

### Final Answer:
The missing term in the pattern is:
\[ 16 \frac{2}{3} \]