If the (18)th term of the AP (b-3,b+2,b+7,\ldots) is (94), what is the value of (b)?

Correct answer: 12

The common difference between consecutive terms is \(5\), so the first term is \(a=b-3\) and \(d=5\). The \(18\)th term is \(a_{18}=a+17d\). Thus, \(94=(b-3)+17\times5=b+82\), which gives \(b=12\). If \(b=11\), the \(18\)th term would be \(93\), so it is not correct. Exam tip: use \(n-1\) common differences when finding the \(n\)th term.