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What is the explicit rule for the sequence (1,4,9,16,\ldots)?
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Answer and explanation
Correct answer: \(a_n=n^2\)
The terms are \(1^2, 2^2, 3^2, 4^2,\ldots\). Therefore, the \(n\)th term is \(a_n=n^2\). If \(a_n=n^2+1\), the first term would be 2, which does not match the sequence. Exam tip: write the first few terms alongside \(n=1,2,3,\ldots\) to check the pattern.
Frequently asked questions
What is the correct answer to this question?
\(a_n=n^2\)
Why is this the correct answer?
The terms are \(1^2, 2^2, 3^2, 4^2,\ldots\). Therefore, the \(n\)th term is \(a_n=n^2\). If \(a_n=n^2+1\), the first term would be 2, which does not match the sequence. Exam tip: write the first few terms alongside \(n=1,2,3,\ldots\) to check the pattern.
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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