What is the general term of the sequence (1,2,5,10,\ldots)?
Answer and explanation
Correct answer: \(a_n=n^2-2n+2\)
For \(a_n=n^2-2n+2\), substituting \(n=1,2,3,4\) gives \(1,2,5,10\), respectively. Hence, it is the required general term. Option B gives the first term as \(2\), so it cannot represent the sequence. In an exam, verify a proposed general term by substituting the first few values of \(n\).
Frequently asked questions
What is the correct answer to this question?
\(a_n=n^2-2n+2\)
Why is this the correct answer?
For \(a_n=n^2-2n+2\), substituting \(n=1,2,3,4\) gives \(1,2,5,10\), respectively. Hence, it is the required general term. Option B gives the first term as \(2\), so it cannot represent the sequence. In an exam, verify a proposed general term by substituting the first few 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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