Which general term is correct for the sequence (6,13,22,33,\ldots)?
Answer and explanation
Correct answer: \(a_n=n^2+4n+1\)
For option A, substituting \(n=1,2,3,4\) gives \(6,13,22,33\), respectively. Hence, the correct general term is \(a_n=n^2+4n+1\). The closest distractor, option D, gives the first two terms as \(6,13\), but for \(n=3\) it gives \(20\), not \(22\). Exam tip: test a proposed general term using at least the first three values of \(n\).
Frequently asked questions
What is the correct answer to this question?
\(a_n=n^2+4n+1\)
Why is this the correct answer?
For option A, substituting \(n=1,2,3,4\) gives \(6,13,22,33\), respectively. Hence, the correct general term is \(a_n=n^2+4n+1\). The closest distractor, option D, gives the first two terms as \(6,13\), but for \(n=3\) it gives \(20\), not \(22\). Exam tip: test 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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