What is the general term of the sequence (3,12,27,48,\ldots)?
Answer and explanation
Correct answer: \(a_n=3n^2\)
Substituting \(n=1,2,3,4\) in \(a_n=3n^2\) gives \(3,12,27,48\), respectively. Therefore, the correct general term is \(a_n=3n^2\). Although \(a_n=3n\) looks related, it gives \(3,6,9,12\), so it is not correct. 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?
\(a_n=3n^2\)
Why is this the correct answer?
Substituting \(n=1,2,3,4\) in \(a_n=3n^2\) gives \(3,12,27,48\), respectively. Therefore, the correct general term is \(a_n=3n^2\). Although \(a_n=3n\) looks related, it gives \(3,6,9,12\), so it is not correct. 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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