What is the general term of the sequence (3,12,35,96,\ldots)?
Answer and explanation
Correct answer: \(a_n=3^n+n^2-1\)
The correct rule is \(a_n=3^n+n^2-1\). Substituting \(n=1,2,3,4\) gives \(3,12,35,96\), respectively. Although \(a_n=3n^2\) gives the first two terms as 3 and 12, it gives 27 as the third term instead of 35, so it is not the rule for the sequence. In exams, test a proposed general term with at least the first three terms.
Frequently asked questions
What is the correct answer to this question?
\(a_n=3^n+n^2-1\)
Why is this the correct answer?
The correct rule is \(a_n=3^n+n^2-1\). Substituting \(n=1,2,3,4\) gives \(3,12,35,96\), respectively. Although \(a_n=3n^2\) gives the first two terms as 3 and 12, it gives 27 as the third term instead of 35, so it is not the rule for the sequence. In exams, test a proposed general term with 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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