Which is the correct rule for the sequence (3,6,11,18,\ldots)?
Answer and explanation
Correct answer: \(a_n=n^2+2\)
Substituting \(n=1,2,3,4\) into \(a_n=n^2+2\) gives \(3,6,11,18\), respectively. The successive differences are \(3,5,7\), which are odd numbers, indicating a square-based sequence. In contrast, \(a_n=n^2+1\) gives the first term as \(2\), so it is not correct. Exam tip: when second differences are constant or first differences are consecutive odd numbers, test a rule involving \(n^2\).
Frequently asked questions
What is the correct answer to this question?
\(a_n=n^2+2\)
Why is this the correct answer?
Substituting \(n=1,2,3,4\) into \(a_n=n^2+2\) gives \(3,6,11,18\), respectively. The successive differences are \(3,5,7\), which are odd numbers, indicating a square-based sequence. In contrast, \(a_n=n^2+1\) gives the first term as \(2\), so it is not correct. Exam tip: when second differences are constant or first differences are consecutive odd numbers, test a rule involving \(n^2\).
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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