What is the (n)th term of the sequence (3,10,21,36,55,\ldots)?
Answer and explanation
Correct answer: \(2n^2+n\)
The successive differences are \(7,11,15,19\), and their second differences are constant at \(4\). Hence the sequence has a quadratic nth-term rule. With \(a_n=2n^2+n\), we get \(a_1=3\), \(a_2=10\), \(a_3=21\), and \(a_4=36\). The close distractor \(2n^2+n-1\) gives the first term as \(2\), not \(3\). Exam tip: a constant second difference usually indicates an \(n^2\)-based rule.
Frequently asked questions
What is the correct answer to this question?
\(2n^2+n\)
Why is this the correct answer?
The successive differences are \(7,11,15,19\), and their second differences are constant at \(4\). Hence the sequence has a quadratic nth-term rule. With \(a_n=2n^2+n\), we get \(a_1=3\), \(a_2=10\), \(a_3=21\), and \(a_4=36\). The close distractor \(2n^2+n-1\) gives the first term as \(2\), not \(3\). Exam tip: a constant second difference usually indicates an \(n^2\)-based 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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