Which explicit rule is correct for the sequence 2, 11/2, 21/2, 17, …?

Correct answer: aₙ = (3n² + 5n)/4

Direct answer: option A. To verify an explicit rule, substitute the position numbers n = 1, 2, 3, and 4. In A, n = 1 gives (3 + 5)/4 = 2. For n = 2, the numerator is 3(4) + 5(2) = 22, so the value is 22/4 = 11/2. For n = 3, the numerator is 3(9) + 5(3) = 42, giving 42/4 = 21/2. For n = 4, the numerator is 3(16) + 5(4) = 68, giving 68/4 = 17. Thus A matches every listed term. B gives 2 when n = 1 but gives 5 when n = 2, not 11/2. C gives 2 at n = 1 but gives 5 at n = 2, so it also fails. D gives (5 + 1)/4 = 3/2 at n = 1, not 2. A formula is accepted only when it reproduces the sequence consistently. Keep the square on n separate from the coefficient while calculating.