What is the (18)th term of the AP \(-7,\frac{-3}{2},4,\ldots\)?

Correct answer: \(\frac{173}{2}\)

The first term is \(a=-7\), and the common difference is \(d=\frac{-3}{2}-(-7)=\frac{11}{2}\). Using \(a_n=a+(n-1)d\), we get \(a_{18}=-7+17\times\frac{11}{2}=\frac{-14+187}{2}=\frac{173}{2}\). Hence, \(\frac{173}{2}\) is correct. The option \(\frac{175}{2}\) can result from a small error in counting terms or arithmetic. Exam tip: for an AP involving fractions, write terms with a common denominator first to check the common difference accurately.