If the first term of an AP is (16) and (a_{26}=116), what is (d)?
Answer and explanation
Correct answer: 4
The nth-term formula of an AP is \(a_n=a+(n-1)d\). Therefore, \(a_{26}=16+25d\). Given \(a_{26}=116\), we get \(116=16+25d\), so \(25d=100\) and hence \(d=4\). If 3 were used, the 26th term would be \(16+25\times3=91\), not 116. Exam tip: in \(a_n\), the common difference is multiplied by \(n-1\), not by \(n\).
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
The nth-term formula of an AP is \(a_n=a+(n-1)d\). Therefore, \(a_{26}=16+25d\). Given \(a_{26}=116\), we get \(116=16+25d\), so \(25d=100\) and hence \(d=4\). If 3 were used, the 26th term would be \(16+25\times3=91\), not 116. Exam tip: in \(a_n\), the common difference is multiplied by \(n-1\), not by \(n\).
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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