What is the general term of the sequence 12, 27, 46, 69, …?
Answer and explanation
Correct answer: aₙ = 2n² + 9n + 1
The governing concept is finding an explicit quadratic rule from the sequence. The first differences are 15, 19 and 23, which increase by 4, so the second difference is constant and a quadratic formula is expected. Check option A: for n = 1, 2 + 9 + 1 = 12; for n = 2, 8 + 18 + 1 = 27; for n = 3, 18 + 27 + 1 = 46; and for n = 4, 32 + 36 + 1 = 69. Therefore A matches all four terms. Option B and C are linear and cannot reflect the changing first differences. Option D gives 11 for n = 1 and 28 for n = 2, so it fails immediately.
Frequently asked questions
What is the correct answer to this question?
aₙ = 2n² + 9n + 1
Why is this the correct answer?
The governing concept is finding an explicit quadratic rule from the sequence. The first differences are 15, 19 and 23, which increase by 4, so the second difference is constant and a quadratic formula is expected. Check option A: for n = 1, 2 + 9 + 1 = 12; for n = 2, 8 + 18 + 1 = 27; for n = 3, 18 + 27 + 1 = 46; and for n = 4, 32 + 36 + 1 = 69. Therefore A matches all four terms. Option B and C are linear and cannot reflect the changing first differences. Option D gives 11 for n = 1 and 28 for n = 2, so it fails immediately.
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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