Which general term is correct for the sequence (2,18,52,110,\ldots)?
Answer and explanation
Correct answer: \(a_n=n^3+3n^2-2\)
For \(a_n=n^3+3n^2-2\), substituting \(n=1,2,3,4\) gives \(2,18,52,110\), respectively. Hence, it is the correct general term. The close distractor \(2n^3\) gives the first term as 2, but gives 16 rather than 18 when \(n=2\). In an exam, verify a proposed general term using at least the first two or three terms.
Frequently asked questions
What is the correct answer to this question?
\(a_n=n^3+3n^2-2\)
Why is this the correct answer?
For \(a_n=n^3+3n^2-2\), substituting \(n=1,2,3,4\) gives \(2,18,52,110\), respectively. Hence, it is the correct general term. The close distractor \(2n^3\) gives the first term as 2, but gives 16 rather than 18 when \(n=2\). In an exam, verify a proposed general term using at least the first two or 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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