What is the general term of the sequence (5,16,33,56,\ldots)?
Answer and explanation
Correct answer: \(a_n=3n^2+2n\)
For \(a_n=3n^2+2n\), substituting \(n=1,2,3,4\) gives \(5,16,33,56\), respectively. Hence, it is the required general term. Although \(a_n=2n^2+3n\) gives the first term as 5, it gives 14 as the second term, not 16. Exam tip: verify a proposed general term by checking at least the first two or three values of \(n\).
Frequently asked questions
What is the correct answer to this question?
\(a_n=3n^2+2n\)
Why is this the correct answer?
For \(a_n=3n^2+2n\), substituting \(n=1,2,3,4\) gives \(5,16,33,56\), respectively. Hence, it is the required general term. Although \(a_n=2n^2+3n\) gives the first term as 5, it gives 14 as the second term, not 16. Exam tip: verify a proposed general term by checking at least the first two or 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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