What will be the (46)th term of the AP \(13,\frac{39}{2},26,\ldots\)?
Answer and explanation
Correct answer: \(\frac{611}{2}\)
The first term is \(a=13\), and the common difference is \(d=\frac{39}{2}-13=\frac{13}{2}\). The \(n\)th term of an AP is \(a_n=a+(n-1)d\). Therefore, \(a_{46}=13+45\times\frac{13}{2}=\frac{26+585}{2}=\frac{611}{2}\). Hence, option B is correct. A nearby option such as \(\frac{599}{2}\) can result from using an incorrect number of differences. Exam tip: always use \(n-1\), not \(n\), in the nth-term formula.
Frequently asked questions
What is the correct answer to this question?
\(\frac{611}{2}\)
Why is this the correct answer?
The first term is \(a=13\), and the common difference is \(d=\frac{39}{2}-13=\frac{13}{2}\). The \(n\)th term of an AP is \(a_n=a+(n-1)d\). Therefore, \(a_{46}=13+45\times\frac{13}{2}=\frac{26+585}{2}=\frac{611}{2}\). Hence, option B is correct. A nearby option such as \(\frac{599}{2}\) can result from using an incorrect number of differences. Exam tip: always use \(n-1\), not \(n\), in the nth-term formula.
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.
