What will be the (38)th term of the AP \(8,\frac{25}{2},17,\ldots\)?

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 \(a+nd\).