2 Predict how many matchsticks will be needed for Pattern 10. Explain how you get your answer. 3.3 Write down the general rule for the pattern in the form T_n=

You're on a roll — Here are the solutions for Activity 4: 3.2 Predict how many matchsticks will be needed for Pattern 10. Explain how you get your answer. Step 1: Determine the pattern for the number of matchsticks. Let T_n be the number of matchsticks for Figure n. Figure 1: 1 × 1 grid + 1 square on top. Matchsticks = 2(1)(1+1) + 3 = 4 + 3 = 7. Figure 2: 2 × 2 grid + 1 square on top. Matchsticks = 2(2)(2+1) + 3 = 12 + 3 = 15. Figure 3: 3 × 3 grid + 1 square on top. Matchsticks = 2(3)(3+1) + 3 = 24 + 3 = 27. Figure 4: 4 × 4 grid + 1 square on top. Matchsticks = 2(4)(4+1) + 3 = 40 + 3 = 43. The general rule for the number of matchsticks is T_n = 2n(n+1) + 3. Step 2: Calculate the number of matchsticks for Pattern 10. Substitute n=10 into the formula: T_10 = 2(10)(10+1) + 3 T_10 = 2(10)(11) + 3 T_10 = 220 + 3 T_10 = 223 Number of matches in pattern 10 = 223. This is found by using the general rule T_n = 2n(n+1) + 3, where n is the pattern number. For Pattern 10, we substitute n=10 into the rule. 3.3 Write down the general rule for the pattern in the form T_n= The general rule for the number of matchsticks in Figure n is: T_n = 2n(n+1) + 3 Draw Figure 5 in the space provided. Figure 5 will consist of a 5 × 5 grid of squares, with an additional single square placed on top of the middle square of the top row. Here is a description of Figure 5: • It will be a large square grid of 5 rows and 5 columns. • On top of the middle square of the top row, there will be one additional square. Drop the next question!