What is the \(34\)th term of the AP \(7,\frac{19}{2},12,\ldots\)?

Correct answer: \(\frac{179}{2}\)

The first term is \(a=7\), and the common difference is \(d=\frac{19}{2}-7=\frac{5}{2}\). Hence, \(a_{34}=a+(34-1)d=7+33\times\frac{5}{2}=\frac{179}{2}\). Therefore, \(\frac{179}{2}\) is correct. Getting 89 is a common error caused by not handling the denominator 2 correctly while adding 7. Exam tip: always use \(a_n=a+(n-1)d\), not \(a+nd\).