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
Step 1: Set up equations for the given terms of the A.P. The formula for the n-th term of an Arithmetic Progression (A.P.) is a_n = a + (n-1)d, where a is the first term and d is the common difference. Given a_5 = -12: a + (5-1)d = -12 a + 4d = -12 (*) Given a_10 = -27: a + (10-1)d = -27 a + 9d = -27 (**) Step 2: Solve the system of equations to find the common difference d. Subtract equation () from equation (*): (a + 9d) - (a + 4d) = -27 - (-12) 5d = -27 + 12 5d = -15 d = (-15)/(5) d = -3 Step 3: Substitute the value of d into equation (*) to find the first term a. a + 4(-3) = -12 a - 12 = -12 a = -12 + 12 a = 0 Step 4: Write the A.P. The first term is a=0 and the common difference is d=-3. The A.P. is a, a+d, a+2d, 0, 0+(-3), 0+2(-3), 0, -3, -6, Step 5: Calculate the 15th term (a_15). Using the formula a_n = a + (n-1)d: a_15 = 0 + (15-1)(-3) a_15 = 0 + (14)(-3) a_15 = -42 The A.P. is 0, -3, -6, and its 15th term is -42. Send me the next one 📸