What is the (n)th term of the sequence (3,11,23,39,59,\ldots)?
Answer and explanation
Correct answer: \(2n^2+2n-1\)
The successive differences are \(8,12,16,20\), and their second differences are all \(4\). Hence, the nth term has a quadratic form. Substituting \(n=1,2,3\) in \(a_n=2n^2+2n-1\) gives \(3,11,23\), so this is the correct rule. The close distractor \(2n^2+n\) gives the first term as 3 but gives 10, not 11, when \(n=2\). Exam tip: equal second differences usually indicate a rule of the form \(an^2+bn+c\).
Frequently asked questions
What is the correct answer to this question?
\(2n^2+2n-1\)
Why is this the correct answer?
The successive differences are \(8,12,16,20\), and their second differences are all \(4\). Hence, the nth term has a quadratic form. Substituting \(n=1,2,3\) in \(a_n=2n^2+2n-1\) gives \(3,11,23\), so this is the correct rule. The close distractor \(2n^2+n\) gives the first term as 3 but gives 10, not 11, when \(n=2\). Exam tip: equal second differences usually indicate a rule of the form \(an^2+bn+c\).
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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