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 solve this arithmetic progression problem: The formula for the n-th term of an arithmetic progression is a_n = a_1 + (n-1)d, where a_1 is the first term and d is the common difference. Given: a_13 = 10 a_25 = 20 This gives us two equations: 1) a_1 + (13-1)d = 10 a_1 + 12d = 10 2) a_1 + (25-1)d = 20 a_1 + 24d = 20 i) Calculate the common difference Step 1: Subtract equation (1) from equation (2). (a_1 + 24d) - (a_1 + 12d) = 20 - 10 12d = 10 Step 2: Solve for d. d = (10)/(12) d = (5)/(6) ii) Calculate the first term Step 3: Substitute the value of d into equation (1). a_1 + 12((5)/(6)) = 10 a_1 + 2 × 5 = 10 a_1 + 10 = 10 Step 4: Solve for a_1. a_1 = 10 - 10 a_1 = 0 iii) Calculate the 17th term Step 5: Use the formula for the n-th term with n=17, a_1=0, and d=(5)/(6). a_17 = a_1 + (17-1)d a_17 = 0 + 16((5)/(6)) Step 6: Simplify the expression. a_17 = (16 × 5)/(6) a_17 = (80)/(6) a_17 = (40)/(3) That's 2 down. 3 left today — send the next one.