Which general term is correct for the sequence (2,5,10,17,\ldots)?
Answer and explanation
Correct answer: \(a_n=n^2+1\)
For \(n=1\), \(a_1=1^2+1=2\); for \(n=2\), \(a_2=2^2+1=5\); and for \(n=3\), \(a_3=3^2+1=10\). Hence, the correct general term is \(a_n=n^2+1\). The close option \(a_n=n^2\) gives the first term as 1, not 2. In an exam, substitute \(n=1,2,3\) to verify a proposed general term quickly.
Frequently asked questions
What is the correct answer to this question?
\(a_n=n^2+1\)
Why is this the correct answer?
For \(n=1\), \(a_1=1^2+1=2\); for \(n=2\), \(a_2=2^2+1=5\); and for \(n=3\), \(a_3=3^2+1=10\). Hence, the correct general term is \(a_n=n^2+1\). The close option \(a_n=n^2\) gives the first term as 1, not 2. In an exam, substitute \(n=1,2,3\) to verify a proposed general term quickly.
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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