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
Welcome back Yonwaba — been a while! Let's pick up where you left off. Here are the solutions to the number pattern questions: 2.1 Complete lines 5 and 6 in the number pattern below: Step 1: Identify the pattern. The pattern shows the sum of consecutive odd numbers starting from 1. Line n sums the first n odd numbers. The sum for Line n is n^2. The last number in Line n is the n-th odd number, given by 2n-1. Step 2: Complete Line 5. Line 5 will sum the first 5 odd numbers. The 5th odd number is 2(5)-1 = 9. The sum for Line 5 is 5^2 = 25. Line 5: 1+3+5+7+9 = 25 = 5 × 5 Step 3: Complete Line 6. Line 6 will sum the first 6 odd numbers. The 6th odd number is 2(6)-1 = 11. The sum for Line 6 is 6^2 = 36. Line 6: 1+3+5+7+9+11 = 36 = 6 × 6 The completed lines are: Line 5: 1+3+5+7+9 = 25 = 5 × 5 Line 6: 1+3+5+7+9+11 = 36 = 6 × 6 2.2 In Line 4 the last number in the pattern is 7. What would be the last number in Line 10? Step 1: Determine the formula for the last number. The last number in Line n is the n-th odd number, which is given by the formula 2n-1. Step 2: Calculate the last number for Line 10. For Line 10, n=10. Last number = 2(10)-1 = 20-1 = 19. The last number in Line 10 would be 19. 2.3 What would all of the numbers in the pattern add up to in Line 12? Step 1: Determine the formula for the sum. The sum of the numbers in Line n is n^2. Step 2: Calculate the sum for Line 12. For Line 12, n=12. Sum = 12^2 = 144. All the numbers in Line 12 would add up to 144. 2.4 Use what you have found above to describe a quick way of adding up the first 20 odd numbers. Step 1: Apply the observed pattern. From the pattern, the sum of the first n odd numbers is n^2. Step 2: Describe the quick way. To add up the first 20 odd numbers, you simply square the number of odd numbers, which is 20. So, the sum is 20^2 = 400. The quick way to add up the first 20 odd numbers is to square the number 20, which gives 400. Send me the next one 📸