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: Identify the given values and the formula for the n-th term of an Arithmetic Progression (AP). The first term, a = -3. The last term, L = 393. The total number of terms, n = 100. The formula for the n-th term is T_n = a + (n-1)d, where d is the common difference. Step 2: Use the last term to find the common difference (d). The last term is the 100th term, so T_100 = 393. Substitute the values into the formula: 393 = -3 + (100-1)d 393 = -3 + 99d Add 3 to both sides: 393 + 3 = 99d 396 = 99d Divide by 99 to find d: d = (396)/(99) d = 4 Step 3: Calculate the 33rd term (T_33). Now that we have the common difference d=4, we can find the 33rd term using the formula T_n = a + (n-1)d with n=33. T_33 = -3 + (33-1)(4) T_33 = -3 + (32)(4) T_33 = -3 + 128 T_33 = 125 The 33rd term of the AP is 125. That's 2 down. 3 left today — send the next one.