Answer:To find the first five terms of the sequence defined by t_n = 3n^2 + 1, we substitute n = 1, 2, 3, 4, 5 into the formula: - For n=1: t_1 = 3(1)^2 + 1 = 3(1) + 1 = 4- For n=2: t_2 = 3(2)^2 + 1 = 3(4) + 1 = 13- For n=3: t_3 = 3(3)^2 + 1 = 3(9) + 1 = 28- For n=4: t_4 = 3(4)^2 + 1 = 3(16) + 1 = 49- For n=5: t_5 = 3(5)^2 + 1 = 3(25) + 1 = 76 Therefore, the first five terms of the sequence are 4, 13, 28, 49, 76.