Which is the correct rule for the sequence (6,14,24,36,\ldots)?
Answer and explanation
Correct answer: \(a_n=n^2+5n\)
The correct rule is \(a_n=n^2+5n\). Substituting \(n=1,2,3,4\) gives \(6,14,24,36\), respectively. Also, the first differences are \(8,10,12\), whose differences are \(2\); hence the sequence should have a quadratic rule. Option B gives the first term as 6, but for \(n=2\) it gives 12, not 14. Exam tip: test a proposed rule with at least the first three values, \(n=1,2,3\).
Frequently asked questions
What is the correct answer to this question?
\(a_n=n^2+5n\)
Why is this the correct answer?
The correct rule is \(a_n=n^2+5n\). Substituting \(n=1,2,3,4\) gives \(6,14,24,36\), respectively. Also, the first differences are \(8,10,12\), whose differences are \(2\); hence the sequence should have a quadratic rule. Option B gives the first term as 6, but for \(n=2\) it gives 12, not 14. Exam tip: test a proposed rule with at least the first three values, \(n=1,2,3\).
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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