Which general term is correct for the sequence (4,9,16,25,\ldots)?
Answer and explanation
Correct answer: \(a_n=(n+1)^2\)
The terms \(4,9,16,25\) are respectively \(2^2,3^2,4^2,5^2\). When \(n=1\), the number being squared is \(2=n+1\); hence the general term is \(a_n=(n+1)^2\). Although \(a_n=n^2+3\) gives 4 for the first term, it gives 7, not 9, when \(n=2\). Exam tip: verify a general term by substituting \(n=1\) and \(n=2\).
Frequently asked questions
What is the correct answer to this question?
\(a_n=(n+1)^2\)
Why is this the correct answer?
The terms \(4,9,16,25\) are respectively \(2^2,3^2,4^2,5^2\). When \(n=1\), the number being squared is \(2=n+1\); hence the general term is \(a_n=(n+1)^2\). Although \(a_n=n^2+3\) gives 4 for the first term, it gives 7, not 9, when \(n=2\). Exam tip: verify a general term by substituting \(n=1\) and \(n=2\).
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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