Which is the (n)th term of the sequence (1,7,17,31,49,\ldots)?
Answer and explanation
Correct answer: \(2n^2-1\)
The consecutive differences are \(6,10,14,18\), and their second differences are constantly \(4\). Hence, the nth term is quadratic in \(n\). Substituting \(n=1,2,3\) in \(2n^2-1\) gives \(1,7,17\), respectively, so it matches the sequence. The close distractor \(2n^2+n-2\) gives \(8\) when \(n=2\), not the required second term \(7\). Exam tip: a constant second difference usually indicates a quadratic nth-term rule.
Frequently asked questions
What is the correct answer to this question?
\(2n^2-1\)
Why is this the correct answer?
The consecutive differences are \(6,10,14,18\), and their second differences are constantly \(4\). Hence, the nth term is quadratic in \(n\). Substituting \(n=1,2,3\) in \(2n^2-1\) gives \(1,7,17\), respectively, so it matches the sequence. The close distractor \(2n^2+n-2\) gives \(8\) when \(n=2\), not the required second term \(7\). Exam tip: a constant second difference usually indicates a quadratic nth-term rule.
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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