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
Here's how to find the common difference: The formula for the n-th term of an arithmetic progression (AP) is: aₙ = a₁ + (n - 1)d where: aₙ is the n-th term a₁ is the first term n is the term number d is the common difference Step 1: Identify the given values. We are given: The sixth term (a₆) = 11 The first term (a₁) = 1 The term number (n) = 6 Step 2: Substitute the values into the formula. a₆ = a₁ + (6 - 1)d 11 = 1 + (5)d Step 3: Solve for the common difference (d). 11 = 1 + 5d Subtract 1 from both sides: 11 - 1 = 5d 10 = 5d Divide by 5: d = 10 / 5 d = 2 The common difference is 2. Comparing this with the given options: A. 2 B. 1/2 C. 1/4 D. 4 The correct option is A. The final answer is A. 2.