Which is the (n)th term of the sequence (4,9,16,25,\ldots)?
Answer and explanation
Correct answer: \((n+1)^2\)
Write the terms as squares: \(4=2^2\), \(9=3^2\), \(16=4^2\), and \(25=5^2\). Since the first term is \(2^2\), the \(n\)th term is \((n+1)^2\). Using \(n^2\) would give the first term as \(1\), which does not match the sequence. Exam tip: always test a proposed nth-term formula with \(n=1\).
Frequently asked questions
What is the correct answer to this question?
\((n+1)^2\)
Why is this the correct answer?
Write the terms as squares: \(4=2^2\), \(9=3^2\), \(16=4^2\), and \(25=5^2\). Since the first term is \(2^2\), the \(n\)th term is \((n+1)^2\). Using \(n^2\) would give the first term as \(1\), which does not match the sequence. Exam tip: always test a proposed nth-term formula with \(n=1\).
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: nth term.
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