What is the general term of the sequence (3,15,35,63,\ldots)?
Answer and explanation
Correct answer: \(a_n=4n^2-1\)
Substituting \(n=1,2,3,4\) in \(a_n=4n^2-1\) gives \(3,15,35,63\), respectively. Hence, the correct general term is \(4n^2-1\). Although \(a_n=3n^2\) gives the first term as 3, its second term is 12, not 15. Exam tip: verify a proposed general term by checking at least the first three values of \(n\).
Frequently asked questions
What is the correct answer to this question?
\(a_n=4n^2-1\)
Why is this the correct answer?
Substituting \(n=1,2,3,4\) in \(a_n=4n^2-1\) gives \(3,15,35,63\), respectively. Hence, the correct general term is \(4n^2-1\). Although \(a_n=3n^2\) gives the first term as 3, its second term is 12, not 15. Exam tip: verify a proposed general term by checking 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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