Question: Complete the sequence below by filling in the missing numbers.
1
18
,
2
17
,
\boxed{\phantom{0}}
16
,
4
\boxed{\phantom{0}}
,
\boxed{\phantom{0}}
\boxed{\phantom{0}}
,
...
1. **State the problem:** We have a sequence of fractions arranged in pairs: $$\frac{1}{18}, \frac{2}{17}, \frac{\boxed{\phantom{0}}}{16}, \frac{4}{\boxed{\phantom{0}}}, \frac{\boxed{\phantom{0}}}{\boxed{\phantom{0}}}, ...$$ and we need to find the missing numbers.
2. **Analyze the pattern:** Notice the numerators and denominators in the given fractions:
- Numerators: 1, 2, ?, 4, ?, ...
- Denominators: 18, 17, 16, ?, ?, ...
3. **Identify the pattern in denominators:** The denominators decrease by 1 each time: 18, 17, 16, ... so the next denominators are 15, 14, ...
4. **Identify the pattern in numerators:** The numerators increase by 1 each time: 1, 2, ?, 4, ... so the missing numerator after 2 is 3.
5. **Fill in the missing numbers:**
- Third fraction: numerator 3, denominator 16 → $$\frac{3}{16}$$
- Fourth fraction: numerator 4, denominator 15 → $$\frac{4}{15}$$
- Fifth fraction: numerator 5, denominator 14 → $$\frac{5}{14}$$
6. **Final completed sequence:**
$$\frac{1}{18}, \frac{2}{17}, \frac{3}{16}, \frac{4}{15}, \frac{5}{14}, ...$$
**Answer:** The missing numbers are 3, 15, 5, and 14.