If aₙ = n² + 3n + 2, what are the first four terms?

Correct answer: 6, 12, 20, 30

Direct answer: option D, 6, 12, 20, 30. An explicit rule gives a term directly when we know its position. The first four positions are n = 1, 2, 3, and 4. Substitute each value carefully into aₙ = n² + 3n + 2. For n = 1, a₁ = 1² + 3(1) + 2 = 6. For n = 2, a₂ = 2² + 3(2) + 2 = 4 + 6 + 2 = 12. For n = 3, a₃ = 9 + 9 + 2 = 20. For n = 4, a₄ = 16 + 12 + 2 = 30. Thus D matches every term. A gives 4 as its first value, so it misuses the formula. B gives 5 first and 21 third, so its substitutions are wrong. C has the correct first term but incorrect later calculations. D is the only complete match. Memory cue: for a first-term question, begin with n = 1, not n = 0, unless the question explicitly says otherwise.