What is the (n)th term of the sequence (13,9,5,1,-3,\ldots)?
Answer and explanation
Correct answer: \(17-4n\)
This is an arithmetic sequence because the common difference between consecutive terms is \(-4\). Here, the first term is \(a=13\) and \(d=-4\). Therefore, \(a_n=a+(n-1)d=13+(n-1)(-4)=17-4n\). Hence, \(17-4n\) is correct. In \(13-4n\), substituting \(n=1\) gives 9 instead of the first term 13. Exam tip: Always substitute \(n=1\) to check whether a proposed nth-term formula gives the first term.
Frequently asked questions
What is the correct answer to this question?
\(17-4n\)
Why is this the correct answer?
This is an arithmetic sequence because the common difference between consecutive terms is \(-4\). Here, the first term is \(a=13\) and \(d=-4\). Therefore, \(a_n=a+(n-1)d=13+(n-1)(-4)=17-4n\). Hence, \(17-4n\) is correct. In \(13-4n\), substituting \(n=1\) gives 9 instead of the first term 13. Exam tip: Always substitute \(n=1\) to check whether a proposed nth-term formula gives the first term.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: nth term.
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