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: Understand the property of an Arithmetic Progression (A.P.). In an Arithmetic Progression, the difference between any two consecutive terms is constant. If a, b, and c are consecutive terms of an A.P., then b - a = c - b. Step 2: Apply the property to the given terms. Given the consecutive terms are (4x - 1), (2x + 5), and (5x + 11). Let a = 4x - 1, b = 2x + 5, and c = 5x + 11. So, we can write the equation: (2x + 5) - (4x - 1) = (5x + 11) - (2x + 5) Step 3: Simplify both sides of the equation. For the left side: 2x + 5 - 4x + 1 = -2x + 6 For the right side: 5x + 11 - 2x - 5 = 3x + 6 Now the equation is: -2x + 6 = 3x + 6 Step 4: Solve the equation for x. Subtract 3x from both sides: -2x - 3x + 6 = 6 -5x + 6 = 6 Subtract 6 from both sides: -5x = 6 - 6 -5x = 0 Divide by -5: x = (0)/(-5) x = 0 x=0 3 done, 2 left today. You're making progress.