Which is the correct rule for the sequence (6,13,22,33,\ldots)?
Answer and explanation
Correct answer: \(a_n=n^2+4n+1\)
The correct rule is \(a_n=n^2+4n+1\). Substituting \(n=1,2,3,4\) gives \(6,13,22,33\), respectively. The first differences are \(7,9,11\), so the constant second difference is \(2\), indicating a quadratic rule. In option B, the second term is \(14\), not the given \(13\). Exam tip: verify a general-term rule by substituting \(n=1,2,3\) and checking the first few terms.
Frequently asked questions
What is the correct answer to this question?
\(a_n=n^2+4n+1\)
Why is this the correct answer?
The correct rule is \(a_n=n^2+4n+1\). Substituting \(n=1,2,3,4\) gives \(6,13,22,33\), respectively. The first differences are \(7,9,11\), so the constant second difference is \(2\), indicating a quadratic rule. In option B, the second term is \(14\), not the given \(13\). Exam tip: verify a general-term rule by substituting \(n=1,2,3\) and checking the first few 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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