What is the general term of the sequence (3,10,21,36,\ldots)?
Answer and explanation
Correct answer: \(a_n=2n^2+n\)
The first differences are \(7,11,15\), and the second difference is constant at \(4\), so the general term should be quadratic. Substituting \(n=1,2,3,4\) in \(a_n=2n^2+n\) gives \(3,10,21,36\), respectively. Option A gives the first term as \(3\), but its second term is \(8\), not \(10\). Exam tip: verify a proposed general term using at least the first three terms.
Frequently asked questions
What is the correct answer to this question?
\(a_n=2n^2+n\)
Why is this the correct answer?
The first differences are \(7,11,15\), and the second difference is constant at \(4\), so the general term should be quadratic. Substituting \(n=1,2,3,4\) in \(a_n=2n^2+n\) gives \(3,10,21,36\), respectively. Option A gives the first term as \(3\), but its second term is \(8\), not \(10\). Exam tip: verify a proposed general term using at least the first three terms.
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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