What is the general term of the sequence (4,22,66,148,\ldots)?
Answer and explanation
Correct answer: \(a_n=2n^3+n^2+n\)
The correct rule is \(a_n=2n^3+n^2+n\). Substituting \(n=1,2,3,4\) gives \(4,22,66,148\), respectively. The closest distractor, \(4n^2\), gives 4 when \(n=1\), but it gives 16 rather than 22 when \(n=2\). Exam tip: verify a proposed general term using at least the first three terms.
Frequently asked questions
What is the correct answer to this question?
\(a_n=2n^3+n^2+n\)
Why is this the correct answer?
The correct rule is \(a_n=2n^3+n^2+n\). Substituting \(n=1,2,3,4\) gives \(4,22,66,148\), respectively. The closest distractor, \(4n^2\), gives 4 when \(n=1\), but it gives 16 rather than 22 when \(n=2\). Exam tip: verify a proposed general term using at least the first three 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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