What is the nth term of the sequence 6, 13, 24, 39, 58, …?
Answer and explanation
Correct answer: 2n² + n + 3
The governing concept is using finite differences to identify a quadratic nth-term rule. The first differences are 7, 11, 15, and 19; their second differences are 4, 4, and 4. For a quadratic an² + bn + c, the constant second difference is 2a, so 2a = 4 and a = 2. Testing the remaining coefficients gives option B: at n = 1, 2 + 3 + 1 = 6; at n = 2, 8 + 6 + 1 = 15, which does not match the sequence. Therefore the supplied sequence and option B are inconsistent. In fact, solving from the terms gives aₙ = 2n² + n + 3: it yields 6, 13, 24, 39, 58. Thus option A is the unambiguous correct answer; option B is not correct.
Frequently asked questions
What is the correct answer to this question?
2n² + n + 3
Why is this the correct answer?
The governing concept is using finite differences to identify a quadratic nth-term rule. The first differences are 7, 11, 15, and 19; their second differences are 4, 4, and 4. For a quadratic an² + bn + c, the constant second difference is 2a, so 2a = 4 and a = 2. Testing the remaining coefficients gives option B: at n = 1, 2 + 3 + 1 = 6; at n = 2, 8 + 6 + 1 = 15, which does not match the sequence. Therefore the supplied sequence and option B are inconsistent. In fact, solving from the terms gives aₙ = 2n² + n + 3: it yields 6, 13, 24, 39, 58. Thus option A is the unambiguous correct answer; option B is not correct.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: nth term.
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