What is the general term of the sequence (2,12,36,80,\ldots)?
Answer and explanation
Correct answer: \(a_n=n^3+n^2\)
For \(a_n=n^3+n^2\), substituting \(n=1,2,3,4\) gives \(2,12,36,80\), respectively. Hence, this is the general term of the sequence. The close distractor \(4n^2-2n\) gives 2 and 12 initially, but for \(n=3\) it gives 30, not 36. Exam tip: verify a proposed general term using at least the first three values of \(n\).
Frequently asked questions
What is the correct answer to this question?
\(a_n=n^3+n^2\)
Why is this the correct answer?
For \(a_n=n^3+n^2\), substituting \(n=1,2,3,4\) gives \(2,12,36,80\), respectively. Hence, this is the general term of the sequence. The close distractor \(4n^2-2n\) gives 2 and 12 initially, but for \(n=3\) it gives 30, not 36. Exam tip: verify a proposed general term using at least the first three values of \(n\).
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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