What is the general term of the sequence (9,25,49,81,\ldots)?
Answer and explanation
Correct answer: \(a_n=(2n+1)^2\)
The terms \(9,25,49,81\) are \(3^2,5^2,7^2,9^2\), respectively. They are squares of consecutive odd numbers, represented by \(2n+1\). For \(n=1\), \((2\times1+1)^2=9\). Hence, the general term is \(a_n=(2n+1)^2\). Option B gives \(1\) as its first term, so it does not represent this sequence. Exam tip: verify a general term by substituting \(n=1\) and \(n=2\).
Frequently asked questions
What is the correct answer to this question?
\(a_n=(2n+1)^2\)
Why is this the correct answer?
The terms \(9,25,49,81\) are \(3^2,5^2,7^2,9^2\), respectively. They are squares of consecutive odd numbers, represented by \(2n+1\). For \(n=1\), \((2\times1+1)^2=9\). Hence, the general term is \(a_n=(2n+1)^2\). Option B gives \(1\) as its first term, so it does not represent this sequence. 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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