1. **Stating the problem:** We have a table showing the number of circles and squares for different figure numbers. We need to find the pattern (talmønsteret) and fill in the missing values for figure 9 and 10. 2. **Analyzing circles:** The circles follow a quadratic pattern. Given: - Figure 3 has 9 circles - Figure 5 has 25 circles - Figure 6 has 36 circles These correspond to $3^2=9$, $5^2=25$, and $6^2=36$. So the formula for circles is: $$\text{Circles} = n^2$$ where $n$ is the figure number. 3. **Calculating circles for figure 9 and 10:** $$\text{Circles at } n=9 = 9^2 = 81$$ $$\text{Circles at } n=10 = 10^2 = 100$$ 4. **Analyzing squares:** The squares given are: - Figure 3: 12 - Figure 5: 20 - Figure 6: 24 We look for a pattern. Let's check if squares relate linearly to $n$: Try $\text{Squares} = 4n$: - For $n=3$, $4\times3=12$ (matches) - For $n=5$, $4\times5=20$ (matches) - For $n=6$, $4\times6=24$ (matches) So the formula for squares is: $$\text{Squares} = 4n$$ 5. **Calculating squares for figure 9 and 10:** $$\text{Squares at } n=9 = 4 \times 9 = 36$$ $$\text{Squares at } n=10 = 4 \times 10 = 40$$ 6. **Final filled table:** | Figur nummer | Sirklar | Kvadrat | |-------------|---------|---------| | 3 | 9 | 12 | | 5 | 25 | 20 | | 6 | 36 | 24 | | 9 | 81 | 36 | | 10 | 100 | 40 |