Which is the (n)th term of the sequence (9,26,51,84,125,\ldots)?
Answer and explanation
Correct answer: \(4n^2+5n\)
The successive differences are \(17,25,33,41\), and their second differences are all \(8\). Hence the nth term is quadratic: \(a_n=4n^2+bn+c\). Substituting \(n=1\) and \(n=2\) gives \(b=5\) and \(c=0\). Therefore, \(a_n=4n^2+5n\). Option C gives 9 for \(n=1\), but it gives 25 rather than 26 for \(n=2\). Exam tip: when second differences are constant, test a form \(an^2+bn+c\).
Frequently asked questions
What is the correct answer to this question?
\(4n^2+5n\)
Why is this the correct answer?
The successive differences are \(17,25,33,41\), and their second differences are all \(8\). Hence the nth term is quadratic: \(a_n=4n^2+bn+c\). Substituting \(n=1\) and \(n=2\) gives \(b=5\) and \(c=0\). Therefore, \(a_n=4n^2+5n\). Option C gives 9 for \(n=1\), but it gives 25 rather than 26 for \(n=2\). Exam tip: when second differences are constant, test a 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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