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
Okay, let's tackle these. Starting with number 7. Step 1: Find the first term, a, by calculating S_1. The sum of the first term is the first term itself. S_1 = 2(1)^2 - 1 S_1 = 2 - 1 a = 1 Step 2: Find the sum of the first two terms, S_2. S_2 = 2(2)^2 - 2 S_2 = 2(4) - 2 S_2 = 8 - 2 S_2 = 6 Step 3: Find the second term, T_2, using the relationship S_2 = T_1 + T_2. Since T_1 = a = 1: 6 = 1 + T_2 T_2 = 6 - 1 T_2 = 5 Step 4: Calculate the common difference, d, using d = T_2 - T_1. d = 5 - 1 d = 4 The first term is 1 and the common difference is 4. That's 2 down. 3 left today — send the next one.