1. **Stating the problem:** We are given a pattern where the number of black squares increases with the pattern number. We need to fill in missing values, draw next patterns, and find the number of black squares for given pattern numbers. 2. **Given table:** | Pattern number (A) | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |--------------------|---|---|---|---|---|---|---|---|---|----| | Number of black squares | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 16 | 18 | 20 | 3. **Formula:** The number of black squares is given by the formula: $$\text{Number of black squares} = 2 \times \text{Pattern number}$$ This means for any pattern number $n$, the number of black squares is $2n$. 4. **Answering each part:** - a) Fill in the blank spaces in the table: | Pattern number (A) | 1 | 2 | 3 | 4 | |--------------------|---|---|---|---| | Number of black squares | 2 | 4 | 6 | 8 | - b) Drawing patterns 5 and 6 is not possible here, but based on the pattern, pattern 5 has 10 black squares and pattern 6 has 12 black squares. - c) Number of black squares in pattern 5: $$2 \times 5 = 10$$ - d) Number of black squares in pattern 6: $$2 \times 6 = 12$$ - e) Number of black squares in pattern 10: $$2 \times 10 = 20$$ - f) Copying the full table with all values: | Pattern number (A) | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |--------------------|---|---|---|---|---|---|---|---|---|----| | Number of black squares | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 16 | 18 | 20 | **Summary:** The number of black squares doubles the pattern number, so the formula $\text{Number of black squares} = 2 \times \text{Pattern number}$ applies to all patterns.