Determine the constant difference or the constant ratio of the following sequences and state whether the sequence is numeric or geometric.

Thanks for sending the image again, Blessing. Let's finish up this worksheet. 4. The following structures are made of toothpicks and sweets. Complete the table below that describes the relationship between the pattern number and the number of sweets used to keep the structures together. a) The pattern number and the number of sweets used to keep the structures together. Step 1: Count the number of sweets for each pattern. Pattern 1: 6 sweets Pattern 2: 10 sweets Pattern 3: 14 sweets Step 2: Determine the rule for the sequence of sweets. The constant difference is 10-6=4. The rule for the n-th term is T_n = a_1 + (n-1)d = 6 + (n-1)4 = 6 + 4n - 4 = 4n + 2. Step 3: Calculate the number of sweets for pattern numbers 10 and 48. For Pattern 10: T_10 = 4(10) + 2 = 40 + 2 = 42 For Pattern 48: T_48 = 4(48) + 2 = 192 + 2 = 194 b) The pattern number and the number of toothpicks the structure is made of. Step 1: Count the number of toothpicks for each pattern. Pattern 1: 11 toothpicks (3 bottom, 2 top, 4 vertical, 2 slanted) Pattern 2: 20 toothpicks (6 bottom, 4 top, 6 vertical, 4 slanted) Pattern 3: 29 toothpicks (9 bottom, 6 top, 8 vertical, 6 slanted) Step 2: Determine the rule for the sequence of toothpicks. The constant difference is 20-11=9. The rule for the n-th term is T_n = a_1 + (n-1)d = 11 + (n-1)9 = 11 + 9n - 9 = 9n + 2. Step 3: Calculate the number of toothpicks for pattern numbers 10 and 48. For Pattern 10: T_10 = 9(10) + 2 = 90 + 2 = 92 For Pattern 48: T_48 = 9(48) + 2 = 432 + 2 = 434 Step 4: Complete the table. |c|c|c|c|c|c| Pattern number & 1 & 2 & 3 & 10 & 48 \\ Number of sweets & 6 & 10 & 14 & 42 & 194 \\ Number of toothpicks & 11 & 20 & 29 & 92 & 434 \\ 5. Use number sentences to describe the rule and the n term of the following patterns. a) 9; 12; 15; 18; ...; n Step 1: Determine the rule. The difference between consecutive terms is 12-9=3, 15-12=3. The rule is to add 3 to the previous term. Step 2: Find the n-th term. This is an arithmetic sequence with first term a_1=9 and common difference d=3. The formula for the n-th term is T_n = a_1 + (n-1)d. T_n = 9 + (n-1)3 T_n = 9 + 3n - 3 T_n = 3n + 6 b) -5; -7; -9; -11; ...; n Step 1: Determine the rule. The difference between consecutive terms is -7 - (-5) = -2, -9 - (-7) = -2. The rule is to subtract 2 from the previous term. Step 2: Find the n-th term. This is an arithmetic sequence with first term a_1=-5 and common difference d=-2. The formula for the n-th term is T_n = a_1 + (n-1)d. T_n = -5 + (n-1)(-2) T_n = -5 - 2n + 2 T_n = -2n - 3 3 done, 2 left today. You're making progress.