Which general term is correct for the sequence (3,8,17,32,\ldots)?
Answer and explanation
Correct answer: \(a_n=2^n+n^2\)
The term number starts with \(n=1\). Substituting \(n=1,2,3,4\) into \(a_n=2^n+n^2\) gives \(3,8,17,32\), respectively. The close distractor \(2n^2+1\) gives \(3,9\) as its first two terms, so it does not fit the sequence. Exam tip: verify a proposed general term using at least the first three values of \(n\).
Frequently asked questions
What is the correct answer to this question?
\(a_n=2^n+n^2\)
Why is this the correct answer?
The term number starts with \(n=1\). Substituting \(n=1,2,3,4\) into \(a_n=2^n+n^2\) gives \(3,8,17,32\), respectively. The close distractor \(2n^2+1\) gives \(3,9\) as its first two terms, so it does not fit the sequence. Exam tip: verify a proposed general term 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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