What will be the (38)th term of the AP \(8,\frac{25}{2},17,\ldots\)?
Answer and explanation
Correct answer: \(\frac{349}{2}\)
The first term is \(a=8\), and the common difference is \(d=\frac{25}{2}-8=\frac{9}{2}\). Therefore, \(a_{38}=a+(38-1)d=8+37\times\frac{9}{2}=\frac{16+333}{2}=\frac{349}{2}\). Hence, option B is correct. Choosing \(\frac{341}{2}\) results from an error in counting the number of differences or calculating \(d\). Exam tip: for the \(n\)th term, always use \(a_n=a+(n-1)d\), not \(a+nd\).
Frequently asked questions
What is the correct answer to this question?
\(\frac{349}{2}\)
Why is this the correct answer?
The first term is \(a=8\), and the common difference is \(d=\frac{25}{2}-8=\frac{9}{2}\). Therefore, \(a_{38}=a+(38-1)d=8+37\times\frac{9}{2}=\frac{16+333}{2}=\frac{349}{2}\). Hence, option B is correct. Choosing \(\frac{341}{2}\) results from an error in counting the number of differences or calculating \(d\). Exam tip: for the \(n\)th term, always use \(a_n=a+(n-1)d\), not \(a+nd\).
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.
