Which general term is correct for the sequence (4, 10, 18, 28, …)?
Answer and explanation
Correct answer: aₙ = n² + 3n
The terms do not have a constant first difference: the differences are 6, 8, and 10. Their second differences are constant, since 8 − 6 = 2 and 10 − 8 = 2, so a quadratic rule is appropriate. Test option A at the first values of n: when n = 1, a₁ = 1² + 3(1) = 4; when n = 2, a₂ = 2² + 3(2) = 10; when n = 3, a₃ = 9 + 9 = 18; and when n = 4, a₄ = 16 + 12 = 28. Thus option A reproduces all four terms and is correct. Option B and option D are linear, so their differences would be constant. Option C gives 3, 8, 15, 24, not the stated sequence.
Frequently asked questions
What is the correct answer to this question?
aₙ = n² + 3n
Why is this the correct answer?
The terms do not have a constant first difference: the differences are 6, 8, and 10. Their second differences are constant, since 8 − 6 = 2 and 10 − 8 = 2, so a quadratic rule is appropriate. Test option A at the first values of n: when n = 1, a₁ = 1² + 3(1) = 4; when n = 2, a₂ = 2² + 3(2) = 10; when n = 3, a₃ = 9 + 9 = 18; and when n = 4, a₄ = 16 + 12 = 28. Thus option A reproduces all four terms and is correct. Option B and option D are linear, so their differences would be constant. Option C gives 3, 8, 15, 24, not the stated sequence.
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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