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 solutions for each part of question 1: a) Step 1: Find the common difference. The terms are 13, 23, 33, 43. The difference between consecutive terms is 23 - 13 = 10, 33 - 23 = 10, 43 - 33 = 10. The common difference is 10. Step 2: Determine the n^th term. Since the common difference is 10, the n^th term will be of the form 10n + c. For n=1, the term is 13. So, 10(1) + c = 13 10 + c = 13 c = 3. Thus, the n^th term is 10n + 3. Step 3: Calculate the 10^th term. Substitute n=10 into the n^th term formula: T_10 = 10(10) + 3 = 100 + 3 = 103. The n^th term is: 10n + 3 The 10^th term is: 103 b) Step 1: Find the common difference. The terms are 11, 17, 23, 29. The difference between consecutive terms is 17 - 11 = 6, 23 - 17 = 6, 29 - 23 = 6. The common difference is 6. Step 2: Determine the n^th term. Since the common difference is 6, the n^th term will be of the form 6n + c. For n=1, the term is 11. So, 6(1) + c = 11 6 + c = 11 c = 5. Thus, the n^th term is 6n + 5. Step 3: Calculate the 10^th term. Substitute n=10 into the n^th term formula: T_10 = 6(10) + 5 = 60 + 5 = 65. The n^th term is: 6n + 5 The 10^th term is: 65 c) Step 1: Find the common difference. The terms are 17, 20, 23, 26. The difference between consecutive terms is 20 - 17 = 3, 23 - 20 = 3, 26 - 23 = 3. The common difference is 3. Step 2: Determine the n^th term. Since the common difference is 3, the n^th term will be of the form 3n + c. For n=1, the term is 17. So, 3(1) + c = 17 3 + c = 17 c = 14. Thus, the n^th term is 3n + 14. Step 3: Calculate the 10^th term. Substitute n=10 into the n^th term formula: T_10 = 3(10) + 14 = 30 + 14 = 44. The n^th term is: 3n + 14 The 10^th term is: 44 d) Step 1: Find the common difference. The terms are -16, -23, -30, -37. The difference between consecutive terms is -23 - (-16) = -7, -30 - (-23) = -7, -37 - (-30) = -7. The common difference is -7. Step 2: Determine the n^th term. Since the common difference is -7, the n^th term will be of the form -7n + c. For n=1, the term is -16. So, -7(1) + c = -16 -7 + c = -16 c = -9. Thus, the n^th term is -7n - 9. Step 3: Calculate the 10^th term. Substitute n=10 into the n^th term formula: T_10 = -7(10) - 9 = -70 - 9 = -79. The n^th term is: -7n - 9 The 10^th term is: -79 Send me the next one 📸