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What is the general term of the sequence (2,5,10,17,\ldots)?
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Answer and explanation
Correct answer: \(a_n=n^2+1\)
Take \(n=1,2,3,4\). The values of \(n^2\) are \(1,4,9,16\); adding 1 gives \(2,5,10,17\). Hence, \(a_n=n^2+1\). The close distractor \(a_n=n^2+n\) gives 6 when \(n=2\), not 5. Exam tip: verify a proposed general term using at least the first three terms.
Frequently asked questions
What is the correct answer to this question?
\(a_n=n^2+1\)
Why is this the correct answer?
Take \(n=1,2,3,4\). The values of \(n^2\) are \(1,4,9,16\); adding 1 gives \(2,5,10,17\). Hence, \(a_n=n^2+1\). The close distractor \(a_n=n^2+n\) gives 6 when \(n=2\), not 5. Exam tip: verify a proposed general term using at least the first three terms.
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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