If aₙ = n² + 5n + 6, what are the first four terms?
Answer and explanation
Correct answer: 12, 20, 30, 42
The governing concept is generating sequence terms from an explicit formula. Numbering normally begins with n = 1, so evaluate the rule at n = 1, 2, 3, and 4. For n = 1, a₁ = 1² + 5(1) + 6 = 1 + 5 + 6 = 12. For n = 2, a₂ = 2² + 10 + 6 = 20. For n = 3, a₃ = 9 + 15 + 6 = 30. For n = 4, a₄ = 16 + 20 + 6 = 42. Hence the first four terms are 12, 20, 30, 42, so option C is correct. The other choices result from changing the constant, using an incorrect starting index, or making arithmetic errors. It is important to substitute each index carefully and square n before multiplying by 5.
Frequently asked questions
What is the correct answer to this question?
12, 20, 30, 42
Why is this the correct answer?
The governing concept is generating sequence terms from an explicit formula. Numbering normally begins with n = 1, so evaluate the rule at n = 1, 2, 3, and 4. For n = 1, a₁ = 1² + 5(1) + 6 = 1 + 5 + 6 = 12. For n = 2, a₂ = 2² + 10 + 6 = 20. For n = 3, a₃ = 9 + 15 + 6 = 30. For n = 4, a₄ = 16 + 20 + 6 = 42. Hence the first four terms are 12, 20, 30, 42, so option C is correct. The other choices result from changing the constant, using an incorrect starting index, or making arithmetic errors. It is important to substitute each index carefully and square n before multiplying by 5.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Explicit or general rule.
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