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
You're on a roll — To find the first four terms of an AP, we use the formula for the n-th term: a_n = a + (n-1)d, or simply add the common difference d to the previous term. *i) a=10, d=10 Step 1: First term. a_1 = a = 10 Step 2: Second term. a_2 = a_1 + d = 10 + 10 = 20 Step 3: Third term. a_3 = a_2 + d = 20 + 10 = 30 Step 4: Fourth term. a_4 = a_3 + d = 30 + 10 = 40 The first four terms are 10, 20, 30, 40. *ii) a=-2, d=0 Step 1: First term. a_1 = a = -2 Step 2: Second term. a_2 = a_1 + d = -2 + 0 = -2 Step 3: Third term. a_3 = a_2 + d = -2 + 0 = -2 Step 4: Fourth term. a_4 = a_3 + d = -2 + 0 = -2 The first four terms are -2, -2, -2, -2. *iii) a=4, d=-3 Step 1: First term. a_1 = a = 4 Step 2: Second term. a_2 = a_1 + d = 4 + (-3) = 1 Step 3: Third term. a_3 = a_2 + d = 1 + (-3) = -2 Step 4: Fourth term. a_4 = a_3 + d = -2 + (-3) = -5 The first four terms are 4, 1, -2, -5. *iv) a=-1, d=(1)/(2) Step 1: First term. a_1 = a = -1 Step 2: Second term. a_2 = a_1 + d = -1 + (1)/(2) = -(2)/(2) + (1)/(2) = -(1)/(2) Step 3: Third term. a_3 = a_2 + d = -(1)/(2) + (1)/(2) = 0 Step 4: Fourth term. a_4 = a_3 + d = 0 + (1)/(2) = (1)/(2) The first four terms are -1, -(1)/(2), 0, (1)/(2). *v) a=-1.25, d=-0.25 Step 1: First term. a_1 = a = -1.25 Step 2: Second term. a_2 = a_1 + d = -1.25 + (-0.25) = -1.50 Step 3: Third term. a_3 = a_2 + d = -1.50 + (-0.25) = -1.75 Step 4: Fourth term. a_4 = a_3 + d = -1.75 + (-0.25) = -2.00 The first four terms are -1.25, -1.50, -1.75, -2.00. Got more? Send 'em!