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 are the first term and common difference for each AP: *i) 3, 1, -1, -3, Step 1: Identify the first term. The first term is the first number in the sequence. a = 3 Step 2: Calculate the common difference. The common difference d is found by subtracting any term from its succeeding term. d = a_2 - a_1 = 1 - 3 = -2 d = a_3 - a_2 = -1 - 1 = -2 The first term is a = 3 and the common difference is d = -2. *ii) -5, -1, 3, 7, Step 1: Identify the first term. The first term is the first number in the sequence. a = -5 Step 2: Calculate the common difference. d = a_2 - a_1 = -1 - (-5) = -1 + 5 = 4 d = a_3 - a_2 = 3 - (-1) = 3 + 1 = 4 The first term is a = -5 and the common difference is d = 4. *iii) (1)/(3), (5)/(3), (9)/(3), (13)/(3), Step 1: Identify the first term. The first term is the first number in the sequence. a = (1)/(3) Step 2: Calculate the common difference. d = a_2 - a_1 = (5)/(3) - (1)/(3) = (4)/(3) d = a_3 - a_2 = (9)/(3) - (5)/(3) = (4)/(3) The first term is a = (1)/(3) and the common difference is d = (4)/(3). *iv) 0.6, 1.7, 2.8, 3.9, Step 1: Identify the first term. The first term is the first number in the sequence. a = 0.6 Step 2: Calculate the common difference. d = a_2 - a_1 = 1.7 - 0.6 = 1.1 d = a_3 - a_2 = 2.8 - 1.7 = 1.1 The first term is a = 0.6 and the common difference is d = 1.1. 3 done, 2 left today. You're making progress.