Which explicit rule is correct for the sequence (1,14,51,124,\ldots)?
Answer and explanation
Correct answer: \(a_n=2n^3-n\)
Substituting \(n=1,2,3,4\) into \(a_n=2n^3-n\) gives \(1,14,51,124\), respectively. Hence, option B is correct. The close distractor \(n^3+1\) gives 9 when \(n=2\), not the required second term 14. Exam tip: test an explicit rule using at least the first three values of \(n\).
Frequently asked questions
What is the correct answer to this question?
\(a_n=2n^3-n\)
Why is this the correct answer?
Substituting \(n=1,2,3,4\) into \(a_n=2n^3-n\) gives \(1,14,51,124\), respectively. Hence, option B is correct. The close distractor \(n^3+1\) gives 9 when \(n=2\), not the required second term 14. Exam tip: test an explicit rule using at least the first three values of \(n\).
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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