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Which (n)th term is correct for the sequence (2,6,12,20,\ldots)?
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Answer and explanation
Correct answer: \(a_n=n^2+n\)
The rule for this sequence is \(a_n=n(n+1)=n^2+n\). Substituting \(n=1,2,3,4\) gives \(2,6,12,20\), respectively. With \(a_n=n^2\), the second term would be \(4\), not the given \(6\). Exam tip: verify a proposed nth-term rule using the first few terms.
Frequently asked questions
What is the correct answer to this question?
\(a_n=n^2+n\)
Why is this the correct answer?
The rule for this sequence is \(a_n=n(n+1)=n^2+n\). Substituting \(n=1,2,3,4\) gives \(2,6,12,20\), respectively. With \(a_n=n^2\), the second term would be \(4\), not the given \(6\). Exam tip: verify a proposed nth-term rule using the first few terms.
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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