Which is the nth term of the sequence 4, 10, 18, 28, 40, …?

Correct answer: n² + 3n

The governing concept is identifying an explicit formula by testing the position number n against the observed terms. For option C, when n = 1, n² + 3n = 1 + 3 = 4. When n = 2, it gives 4 + 6 = 10; when n = 3, it gives 9 + 9 = 18; when n = 4, it gives 16 + 12 = 28; and when n = 5, it gives 25 + 15 = 40. Thus aₙ = n² + 3n reproduces every listed term, so option C is correct. Option A gives 3 for the first term, option B gives 20 for the third term, and option D gives 5 for the first term. Checking several positions makes the choice reliable rather than based on only one coincidence.