1. **State the problem:** We have a sequence of patterns made from sticks. Each pattern number $n$ has $n$ figures, each figure consisting of a green stick triangle with a short horizontal stick above it. 2. **Analyze the pattern:** - Pattern 1 has 1 figure. - Pattern 2 has 2 figures. - Pattern 3 has 3 figures. 3. **Count sticks per figure:** - Each triangle has 3 sticks. - Each figure has 1 additional horizontal stick above the triangle. - So, each figure has $3 + 1 = 4$ sticks. 4. **Find the total sticks in the $n^{th}$ pattern:** - Since there are $n$ figures, each with 4 sticks, total sticks = $4n$. 5. **Write the rule:** $$\text{Number of sticks in the } n^{th} \text{ pattern} = 4n$$ 6. **Explanation:** The number of sticks grows linearly with the pattern number because each new pattern adds one more figure, and each figure adds 4 sticks. **Final answer:** $$\boxed{4n}$$