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
The solution for x in 2a) is: x = 10 [4]2 The value of x is 10 [4]2. 2b) Given that (2x+1), (7x+1) and (10x+1) are the first three consecutive terms of an AP. Find the value of x and the common difference. Step 1: For an arithmetic progression (AP), the difference between consecutive terms is constant. Let the terms be a_1, a_2, a_3. a_1 = 2x+1 a_2 = 7x+1 a_3 = 10x+1 The common difference d is a_2 - a_1 and a_3 - a_2. Therefore, a_2 - a_1 = a_3 - a_2. Step 2: Set up the equation using the given terms. (7x+1) - (2x+1) = (10x+1) - (7x+1) Step 3: Simplify and solve for x. 7x+1-2x-1 = 10x+1-7x-1 5x = 3x 5x - 3x = 0 2x = 0 x = 0 Step 4: Calculate the common difference d using the value of x. Substitute x=0 into the terms: a_1 = 2(0)+1 = 1 a_2 = 7(0)+1 = 1 a_3 = 10(0)+1 = 1 The common difference d = a_2 - a_1 = 1 - 1 = 0. The value of x is 0 and the common difference is 0.