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
Another one Beloved — let's solve it. Step 1: Write down the given information for the arithmetic progression. 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. We are given: The 10^th term, T_10 = -17. The 18^th term, T_18 = -49. Using the formula, we can set up two equations: For T_10: a + (10-1)d = -17 a + 9d = -17 (*) For T_18: a + (18-1)d = -49 a + 17d = -49 (**) Step 2: Solve the system of equations to find a and d. Subtract equation () from equation (*): (a + 17d) - (a + 9d) = -49 - (-17) 8d = -49 + 17 8d = -32 d = (-32)/(8) d = -4 Substitute d = -4 into equation (*): a + 9(-4) = -17 a - 36 = -17 a = -17 + 36 a = 19 Step 3: Calculate the 27^th term. Now that we have a = 19 and d = -4, we can find T_27: T_27 = a + (27-1)d T_27 = a + 26d T_27 = 19 + 26(-4) T_27 = 19 - 104 T_27 = -85 The 27^th term of the arithmetic progression is -85. Send me the next one 📸