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 descriptions of the patterns and their corresponding number lines: a) 8; 10; 14; 20; 28 Step 1: Analyze the differences between consecutive terms. 10 - 8 = 2 14 - 10 = 4 20 - 14 = 6 28 - 20 = 8 The differences are 2, 4, 6, 8. Step 2: Describe the pattern and draw the number line. The pattern increases by adding a number that increases by 2 each time. Number line: ` 8 10 14 20 28 ---^--^----^------^--------^----------------^---> ` b) 15; 12; 6; -3; -15 Step 1: Analyze the differences between consecutive terms. 12 - 15 = -3 6 - 12 = -6 -3 - 6 = -9 -15 - (-3) = -12 The differences are -3, -6, -9, -12. Step 2: Describe the pattern and draw the number line. The pattern decreases by subtracting a number that increases by 3 each time. Number line: ` -15 -3 6 12 15 <--^------------^---------^------^---^ ` c) 3; 6; 10; 15; 21 Step 1: Analyze the differences between consecutive terms. 6 - 3 = 3 10 - 6 = 4 15 - 10 = 5 21 - 15 = 6 The differences are 3, 4, 5, 6. Step 2: Describe the pattern and draw the number line. The pattern increases by adding a number that increases by 1 each time. Number line: ` 3 6 10 15 21 ---^---^----^-----^-----------^-----------^---> ` d) 10; 9; 7; 4; 0 Step 1: Analyze the differences between consecutive terms. 9 - 10 = -1 7 - 9 = -2 4 - 7 = -3 0 - 4 = -4 The differences are -1, -2, -3, -4. Step 2: Describe the pattern and draw the number line. The pattern decreases by subtracting a number that increases by 1 each time. Number line: ` 0 4 7 9 10 <--^----^---^--^--^ ` That's 2 down. 3 left today — send the next one.