What is the general term of the sequence (9,18,27,36,\ldots)?
Answer and explanation
Correct answer: \(a_n=9n\)
This is an arithmetic progression with first term \(a=9\) and common difference \(d=9\). Thus, \(a_n=a+(n-1)d=9+(n-1)\times9=9n\). Therefore, the correct rule is \(a_n=9n\). The rule \(a_n=9n+1\) gives 10 as the first term, so it is incorrect. Exam tip: substitute \(n=1\) to check whether a proposed rule gives the first term correctly.
Frequently asked questions
What is the correct answer to this question?
\(a_n=9n\)
Why is this the correct answer?
This is an arithmetic progression with first term \(a=9\) and common difference \(d=9\). Thus, \(a_n=a+(n-1)d=9+(n-1)\times9=9n\). Therefore, the correct rule is \(a_n=9n\). The rule \(a_n=9n+1\) gives 10 as the first term, so it is incorrect. Exam tip: substitute \(n=1\) to check whether a proposed rule gives the first term correctly.
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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