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
Let's solve this problem step-by-step. Given: First term (a) = 7 Last term (L) = 43 Sum of the terms (Sₙ) = 250 Step 1: Find the number of terms (n). The formula for the sum of an arithmetic progression when the first and last terms are known is: Sₙ = (n/2)(a + L) Substitute the given values into the formula: 250 = (n/2)(7 + 43) 250 = (n/2)(50) Multiply both sides by 2: 500 = n × 50 Divide by 50 to find n: n = 500 / 50 n = 10 Step 2: Find the common difference (d). The formula for the last term of an arithmetic progression is: L = a + (n - 1)d Substitute the known values (a, L, and the n we just found) into the formula: 43 = 7 + (10 - 1)d 43 = 7 + (9)d Subtract 7 from both sides: 43 - 7 = 9d 36 = 9d Divide by 9 to find d: d = 36 / 9 d = 4 The number of terms is 10 and the common difference is 4. Send me the next one 📸