What is the (n)th term of the sequence (6,20,42,72,110,\ldots)?
Answer and explanation
Correct answer: \(4n^2+2n\)
The consecutive differences are \(14,22,30,38\), and their common second difference is \(8\). Hence the term has the quadratic form \(an^2+bn+c\), where \(2a=8\), so \(a=4\). Using the first two terms gives \(4n^2+2n\). It gives \(6\) for \(n=1\) and \(20\) for \(n=2\). Option B has the correct leading coefficient but incorrect linear and constant terms. Exam tip: for a constant second difference, the coefficient of \(n^2\) is half the second difference.
Frequently asked questions
What is the correct answer to this question?
\(4n^2+2n\)
Why is this the correct answer?
The consecutive differences are \(14,22,30,38\), and their common second difference is \(8\). Hence the term has the quadratic form \(an^2+bn+c\), where \(2a=8\), so \(a=4\). Using the first two terms gives \(4n^2+2n\). It gives \(6\) for \(n=1\) and \(20\) for \(n=2\). Option B has the correct leading coefficient but incorrect linear and constant terms. Exam tip: for a constant second difference, the coefficient of \(n^2\) is half the second difference.
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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