If (a_1=5), (d=7), and (a_{2n+3}=159), what is the value of (n)?
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Answer and explanation
Correct answer: 10
The general term of an AP is \(a_r=a_1+(r-1)d\). Here, putting \(r=2n+3\), we get \(159=5+(2n+2)\times7\). Thus, \(154=14n+14\), so \(14n=140\) and \(n=10\). If 9 is used, the term would be 145, not 159. Exam tip: Substitute the complete expression \(2n+3\) for the index \(r\) in \(a_r\).
Frequently asked questions
What is the correct answer to this question?
10
Why is this the correct answer?
The general term of an AP is \(a_r=a_1+(r-1)d\). Here, putting \(r=2n+3\), we get \(159=5+(2n+2)\times7\). Thus, \(154=14n+14\), so \(14n=140\) and \(n=10\). If 9 is used, the term would be 145, not 159. Exam tip: Substitute the complete expression \(2n+3\) for the index \(r\) in \(a_r\).
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Arithmetic Progressions (AP). Topic: Finding the $n$th term of an AP.
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