1. **Stating the problem:** We have two sequences related to figures: the number of circles (Sirklar) and the number of squares (Kvadrat) for different figure numbers (Figur nummer). We need to find the pattern (talmønsteret) and fill in the missing values in the table. 2. **Analyzing the circles (Sirklar) sequence:** Given values: Figur 3 = 9, Figur 5 = 25, Figur 6 = 36, Figur 9 = 45. 3. **Finding the pattern for circles:** Notice that 9, 25, 36 are perfect squares: $9=3^2$, $25=5^2$, $36=6^2$. But 45 is not a perfect square. Check if 45 fits a pattern: - For Figur 3: $3^2=9$ - For Figur 5: $5^2=25$ - For Figur 6: $6^2=36$ - For Figur 9: Given 45, but $9^2=81$, so 45 is not $9^2$. Check if circles = Figur number \times something: - Figur 3: 9 = 3 \times 3 - Figur 5: 25 = 5 \times 5 - Figur 6: 36 = 6 \times 6 - Figur 9: 45 = 9 \times 5 So for Figur 9, circles = $9 \times 5 = 45$. This suggests the pattern for circles is $\text{Circles} = \text{Figur nummer} \times n$, where $n$ varies. Check if the pattern is circles = Figur number squared for some figures and Figur number times 5 for others. Since 45 = 9 \times 5, maybe the pattern changes after Figur 6. 4. **Analyzing the squares (Kvadrat) sequence:** Given values: Figur 3 = 12, Figur 5 = 20, Figur 6 = 24. Check if squares relate to figure number: - Figur 3: 12 = 3 \times 4 - Figur 5: 20 = 5 \times 4 - Figur 6: 24 = 6 \times 4 So squares = Figur number \times 4. 5. **Filling missing values:** - For Figur 9, squares = $9 \times 4 = 36$. - For Figur 10, circles: since for Figur 9 circles = $9 \times 5$, assume circles = Figur number \times 5 for Figur 9 and 10. So circles for Figur 10 = $10 \times 5 = 50$. - For Figur 10, squares = $10 \times 4 = 40$. 6. **Final table:** | Figur nummer | Sirklar | Kvadrat | |--------------|---------|---------| | 3 | 9 | 12 | | 5 | 25 | 20 | | 6 | 36 | 24 | | 9 | 45 | 36 | | 10 | 50 | 40 | **Answer:** Circles for Figur 10 = 50 Squares for Figur 9 = 36 Squares for Figur 10 = 40