What is the general term of the sequence (0,2,6,12,\ldots)?
Answer and explanation
Correct answer: \(a_n=n^2-n\)
For term numbers \(n=1,2,3,4\), the rule \(n^2-n\) gives \(0,2,6,12\), respectively. Therefore, the correct general term is \(a_n=n^2-n\). The rule \(a_n=2n\) gives 2 as its first term, so it does not match the sequence. Exam tip: verify a general term by substituting \(n=1\) and \(n=2\) and checking the first two terms.
Frequently asked questions
What is the correct answer to this question?
\(a_n=n^2-n\)
Why is this the correct answer?
For term numbers \(n=1,2,3,4\), the rule \(n^2-n\) gives \(0,2,6,12\), respectively. Therefore, the correct general term is \(a_n=n^2-n\). The rule \(a_n=2n\) gives 2 as its first term, so it does not match the sequence. Exam tip: verify a general term by substituting \(n=1\) and \(n=2\) and checking the first two 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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