This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here are the completed tables: a) Step 1: Determine the rule for the sequence. The values are 5, 10, 15, 20. Each term is 5 times its position. The rule is T_n = 5n, where n is the position and T_n is the value of the term. Step 2: Find the value of the term for position 5. For n=5, T_5 = 5 × 5 = 25 Step 3: Find the position in the sequence for the value of term 40. For T_n=40, 5n = 40 n = (40)/(5) = 8 The missing values are 25 for position 5 and 8 for value 40. b) Step 1: Determine the rule for the sequence. The values are 8, 16, 24, 32. Each term is 8 times its position. The rule is T_n = 8n. Step 2: Find the value of the term for position 5. For n=5, T_5 = 8 × 5 = 40 Step 3: Find the position in the sequence for the value of term 150. For T_n=150, 8n = 150 n = (150)/(8) = (75)/(4) = 18.75 The missing values are 40 for position 5 and 18.75 for value 150. c) Step 1: Determine the rule for the sequence. The values are 12, 24, 36, 48. Each term is 12 times its position. The rule is T_n = 12n. Step 2: Find the value of the term for position 5. For n=5, T_5 = 12 × 5 = 60 Step 3: Find the position in the sequence for the value of term 100. For T_n=100, 12n = 100 n = (100)/(12) = (25)/(3) ≈ 8.33 The missing values are 60 for position 5 and (25)/(3) or 8.33 for value 100. d) Step 1: Determine the rule for the sequence. The values are 15, 30, 45, 60. Each term is 15 times its position. The rule is T_n = 15n. Step 2: Find the value of the term for position 5. For n=5, T_5 = 15 × 5 = 75 Step 3: Find the position in the sequence for the value of term 250. For T_n=250, 15n = 250 n = (250)/(15) = (50)/(3) ≈ 16.67 The missing values are 75 for position 5 and (50)/(3) or 16.67 for value 250. e) Step 1: Determine the rule for the sequence. The values are 3, 6, 9, 12. Each term is 3 times its position. The rule is T_n = 3n. Step 2: Find the value of the term for position 5. For n=5, T_5 = 3 × 5 = 15 Step 3: Find the position in the sequence for the value of term 27. For T_n=27, 3n = 27 n = (27)/(3) = 9 The missing values are 15 for position 5 and 9 for value 27. f) Step 1: Determine the rule for the sequence. The values are 10, 20, 30, 40. Each term is 10 times its position. The rule is T_n = 10n. Step 2: Find the value of the term for position 5. For n=5, T_5 = 10 × 5 = 50 Step 3: Find the position in the sequence for the value of term 200. For T_n=200, 10n = 200 n = (200)/(10) = 20 The missing values are 50 for position 5 and 20 for value 200. 3 done, 2 left today. You're making progress.