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
These are arithmetic progressions. The formula for the n^th term of an arithmetic progression is T_n = a + (n-1)d, where a is the first term and d is the common difference. i) Find the 10^th term of 3, 7, 11, 15, Step 1: Identify the first term (a) and the common difference (d). The first term is a = 3. The common difference is d = 7 - 3 = 4. Step 2: Use the formula for the n^th term with n=10. T_10 = a + (10-1)d T_10 = 3 + (9)(4) Step 3: Calculate the 10^th term. T_10 = 3 + 36 T_10 = 39 The 10^th term is 39. ii) Find the 15^th term of 10, 7, 4, 1, Step 1: Identify the first term (a) and the common difference (d). The first term is a = 10. The common difference is d = 7 - 10 = -3. Step 2: Use the formula for the n^th term with n=15. T_15 = a + (15-1)d T_15 = 10 + (14)(-3) Step 3: Calculate the 15^th term. T_15 = 10 - 42 T_15 = -32 The 15^th term is -32. iii) Find the 20^th term of 5, 10, 15, 20, Step 1: Identify the first term (a) and the common difference (d). The first term is a = 5. The common difference is d = 10 - 5 = 5. Step 2: Use the formula for the n^th term with n=20. T_20 = a + (20-1)d T_20 = 5 + (19)(5) Step 3: Calculate the 20^th term. T_20 = 5 + 95 T_20 = 100 The 20^th term is 100. Send me the next one 📸