Which is the general rule for the sequence (2,6,12,20,\ldots)?
Answer and explanation
Correct answer: \(n(n+1)\)
Substituting \(n=1,2,3,4\) in \(n(n+1)\) gives \(1\cdot2=2\), \(2\cdot3=6\), \(3\cdot4=12\), and \(4\cdot5=20\). Hence, the general term is \(a_n=n(n+1)\). The close distractor \(n^2+1\) gives 5 as its second term, so it does not fit the sequence. Exam tip: test a proposed general rule by substituting \(n=1,2,3\) and matching the initial terms.
Frequently asked questions
What is the correct answer to this question?
\(n(n+1)\)
Why is this the correct answer?
Substituting \(n=1,2,3,4\) in \(n(n+1)\) gives \(1\cdot2=2\), \(2\cdot3=6\), \(3\cdot4=12\), and \(4\cdot5=20\). Hence, the general term is \(a_n=n(n+1)\). The close distractor \(n^2+1\) gives 5 as its second term, so it does not fit the sequence. Exam tip: test a proposed general rule by substituting \(n=1,2,3\) and matching the initial 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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