What is the general term of the sequence (5,12,23,38,\ldots)?
Answer and explanation
Correct answer: \(2n^2+n+2\)
Substituting \(n=1,2,3,4\) in \(a_n=2n^2+n+2\) gives \(5,12,23,38\), respectively. Therefore, \(2n^2+n+2\) is the correct general term. The close distractor \(7n-2\) matches the first two terms but gives 19, not 23, for the third term. Exam tip: verify a proposed general term using at least the first three or four terms.
Frequently asked questions
What is the correct answer to this question?
\(2n^2+n+2\)
Why is this the correct answer?
Substituting \(n=1,2,3,4\) in \(a_n=2n^2+n+2\) gives \(5,12,23,38\), respectively. Therefore, \(2n^2+n+2\) is the correct general term. The close distractor \(7n-2\) matches the first two terms but gives 19, not 23, for the third term. Exam tip: verify a proposed general term using at least the first three or four 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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