1. **Stating the problem:** We are given sequences of numbers and corresponding patterns. We need to complete the tables, construct the number sequences for the patterns, and state the pattern rules. 2. **Understanding sequences and patterns:** A sequence is a set of numbers arranged according to a rule or pattern. To find the pattern, observe how the numbers change from one term to the next. --- ### Question 1: Complete the tables (a) Number sequence: 2, 5, 8, 11 - Pattern shows increasing shapes: 1 parallelogram for 2, 3 triangles for 5, 8 parallelograms for 8, 11 parallelograms for 11. - The pattern in numbers increases by 3 each time: $5 - 2 = 3$, $8 - 5 = 3$, $11 - 8 = 3$. (b) Number sequence: 24, 20, 16 - Pattern shows circles arranged in rows of 6 circles each. - For 24: 4 rows of 6 circles ($4 \times 6 = 24$). - For 20: 4 rows of 5 circles ($4 \times 5 = 20$). - For 16: 4 rows of 4 circles ($4 \times 4 = 16$). - The number decreases by 4 each time: $20 - 24 = -4$, $16 - 20 = -4$. (c) Number sequence: 1, 5 - Pattern shows squares clustered: 1 square, then 5 squares arranged in a plus shape. - The pattern suggests adding 4 squares around the center square. --- ### Question 2: Construct the number sequences and state the patterns (a) Sequence: 2, 5, 8, 11, ... - Pattern: Add 3 to the previous number. - Formula: $a_n = 2 + (n-1) \times 3$ - Explanation: Starting at 2, each term increases by 3. (b) Sequence: 24, 20, 16, ... - Pattern: Subtract 4 from the previous number. - Formula: $a_n = 24 - (n-1) \times 4$ - Explanation: Starting at 24, each term decreases by 4. (c) Sequence: 1, 5, 9, 13, ... - Pattern: Add 4 to the previous number. - Formula: $a_n = 1 + (n-1) \times 4$ - Explanation: Starting at 1, each term increases by 4, representing adding squares around the center. --- **Final answers:** (a) Sequence: $2, 5, 8, 11, 14, ...$ Pattern: Add 3 each time. (b) Sequence: $24, 20, 16, 12, 8, ...$ Pattern: Subtract 4 each time. (c) Sequence: $1, 5, 9, 13, 17, ...$ Pattern: Add 4 each time.