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: Recall the formula for the n-th term of an Arithmetic Progression (AP). The formula for the n-th term (T_n) of an AP is given by: T_n = a + (n-1)d where a is the first term, n is the term number, and d is the common difference. Step 2: Identify the given values from the problem. We are given: • The 8th term (T_8) is 25. So, T_n = 25 and n = 8. • The common difference (d) is 2. So, d = 2. We need to find the first term (a). Step 3: Substitute the given values into the formula. 25 = a + (8-1)2 Step 4: Simplify and solve for a. 25 = a + (7)2 25 = a + 14 Subtract 14 from both sides to find a: a = 25 - 14 a = 11 The first term of the AP is 11. 11 3 done, 2 left today. You're making progress.