Which is the correct rule for the sequence (12,25,42,63,\ldots)?
Answer and explanation
Correct answer: \(a_n=2n^2+7n+3\)
For option A, substituting \(n=1,2,3,4\) gives \(12,25,42,63\), respectively. Also, the first differences are \(13,17,21\), so the second differences are constant at \(4\); this supports a quadratic rule. Option C matches the first two terms but gives \(40\), not \(42\), when \(n=3\). Exam tip: test a proposed rule with at least three terms, not just the first term.
Frequently asked questions
What is the correct answer to this question?
\(a_n=2n^2+7n+3\)
Why is this the correct answer?
For option A, substituting \(n=1,2,3,4\) gives \(12,25,42,63\), respectively. Also, the first differences are \(13,17,21\), so the second differences are constant at \(4\); this supports a quadratic rule. Option C matches the first two terms but gives \(40\), not \(42\), when \(n=3\). Exam tip: test a proposed rule with at least three terms, not just the first term.
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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