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
Alright boyufavour — let's do this. Step 1: Write down the given information using the formula for the n^th term of an A.P., T_n = a + (n-1)d. The twelfth term is 7: T_12 = a + (12-1)d a + 11d = 7 (*) The fifteenth term is 9: T_15 = a + (15-1)d a + 14d = 9 (**) Step 2: Subtract equation () from equation (*) to find the common difference d. (a + 14d) - (a + 11d) = 9 - 7 3d = 2 d = (2)/(3) Step 3: Substitute the value of d into equation (*) to find the first term a. a + 11((2)/(3)) = 7 a + (22)/(3) = 7 a = 7 - (22)/(3) a = (21)/(3) - (22)/(3) a = -(1)/(3) The first term is -(1)/(3) and the common difference is (2)/(3). Send me the next one 📸