Which general term is correct for the sequence (4,7,12,19,\ldots)?
Answer and explanation
Correct answer: \(a_n=n^2+3\)
For \(a_n=n^2+3\), substituting \(n=1,2,3,4\) gives \(4,7,12,19\), respectively. Hence, \(a_n=n^2+3\) is the correct general term. Although \(a_n=3n+1\) gives the first two terms 4 and 7, its third term is 10, not 12. Exam tip: test a proposed general term using at least the first three values of \(n\).
Frequently asked questions
What is the correct answer to this question?
\(a_n=n^2+3\)
Why is this the correct answer?
For \(a_n=n^2+3\), substituting \(n=1,2,3,4\) gives \(4,7,12,19\), respectively. Hence, \(a_n=n^2+3\) is the correct general term. Although \(a_n=3n+1\) gives the first two terms 4 and 7, its third term is 10, not 12. Exam tip: test 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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