What is the (n)th term of the sequence (2,5,10,17,26,\ldots)?
Answer and explanation
Correct answer: \(n^2+1\)
Observe that \(2=1^2+1\), \(5=2^2+1\), \(10=3^2+1\), \(17=4^2+1\), and \(26=5^2+1\). Therefore, the \(n\)th term is \(a_n=n^2+1\). The close distractor \(n^2+2\) gives 3 as its first term, so it does not fit. Exam tip: match the terms with squares of \(1,2,3,\ldots\) to identify a quadratic pattern quickly.
Frequently asked questions
What is the correct answer to this question?
\(n^2+1\)
Why is this the correct answer?
Observe that \(2=1^2+1\), \(5=2^2+1\), \(10=3^2+1\), \(17=4^2+1\), and \(26=5^2+1\). Therefore, the \(n\)th term is \(a_n=n^2+1\). The close distractor \(n^2+2\) gives 3 as its first term, so it does not fit. Exam tip: match the terms with squares of \(1,2,3,\ldots\) to identify a quadratic pattern quickly.
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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