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: Identify the pattern. The values of the terms are 10, 20, 30, 40. This is an arithmetic sequence where each term is the position multiplied by 10. Pattern: Value of term = Position × 10. Step 2: Calculate the missing value for position 20. Value of term for position 20 = 20 × 10 = 200. The missing value is 200. b) Step 1: Identify the pattern. The values of the terms are 3, 6, 9, 12. This is an arithmetic sequence where each term is the position multiplied by 3. Pattern: Value of term = Position × 3. Step 2: Calculate the missing value for position 28. Value of term for position 28 = 28 × 3 = 84. The missing value is 84. c) Step 1: Identify the pattern. The values of the terms are 8, 16, 24, 32. This is an arithmetic sequence where each term is the position multiplied by 8. Pattern: Value of term = Position × 8. Step 2: Calculate the missing value for position 16. Value of term for position 16 = 16 × 8 = 128. The missing value is 128. d) Step 1: Identify the pattern. The values of the terms are 12, 24, 36, 48. This is an arithmetic sequence where each term is the position multiplied by 12. Pattern: Value of term = Position × 12. Step 2: Calculate the missing value for position 100. Value of term for position 100 = 100 × 12 = 1200. The missing value is 1200. e) Step 1: Identify the pattern. The values of the terms are 15, 30, 45, 60. This is an arithmetic sequence where each term is the position multiplied by 15. Pattern: Value of term = Position × 15. Step 2: Calculate the missing value for position 30. Value of term for position 30 = 30 × 15 = 450. The missing value is 450. f) Step 1: Identify the pattern. The values of the terms are 1, 8, 27, 64. These are perfect cubes. 1 = 1^3 8 = 2^3 27 = 3^3 64 = 4^3 Pattern: Value of term = Position^3. Step 2: Calculate the missing value for position 50. Value of term for position 50 = 50^3 = 50 × 50 × 50 = 125000. The missing value is 125000. That's 2 down. 3 left today — send the next one.