What is the general term of the sequence (4,8,14,22,\ldots)?
Answer and explanation
Correct answer: \(a_n=n^2+n+2\)
The first differences are \(4,6,8\), and the second differences are constant: \(2,2\). Hence, the general term should be quadratic. Substituting \(n=1,2,3,4\) in \(a_n=n^2+n+2\) gives \(4,8,14,22\), respectively. Although \(n^2+3\) gives the first term as \(4\), it gives \(7\) as the second term, so it is incorrect. Exam tip: when second differences are constant, test a quadratic rule using the first few terms.
Frequently asked questions
What is the correct answer to this question?
\(a_n=n^2+n+2\)
Why is this the correct answer?
The first differences are \(4,6,8\), and the second differences are constant: \(2,2\). Hence, the general term should be quadratic. Substituting \(n=1,2,3,4\) in \(a_n=n^2+n+2\) gives \(4,8,14,22\), respectively. Although \(n^2+3\) gives the first term as \(4\), it gives \(7\) as the second term, so it is incorrect. Exam tip: when second differences are constant, test a quadratic rule using the first few terms.
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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