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Which explicit rule is correct for the sequence (2,15,64,257,\ldots)?
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Answer and explanation
Correct answer: \(a_n=4^n+n-3\)
Substituting \(n=1,2,3,4\) into \(a_n=4^n+n-3\) gives \(2,15,64,257\), respectively. Although \(a_n=n^4+1\) gives the first term as 2, its second term is \(17\), not 15. Exam tip: verify an explicit rule by testing it for at least the first three terms.
Frequently asked questions
What is the correct answer to this question?
\(a_n=4^n+n-3\)
Why is this the correct answer?
Substituting \(n=1,2,3,4\) into \(a_n=4^n+n-3\) gives \(2,15,64,257\), respectively. Although \(a_n=n^4+1\) gives the first term as 2, its second term is \(17\), not 15. Exam tip: verify an explicit rule by testing it for at least the first three 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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