In the AP (58,51,44,\ldots), which is the first term less than (-60)?

Correct answer: -61

The first term is \(a=58\) and the common difference is \(d=-7\). Hence, \(a_n=58+(n-1)(-7)=65-7n\). For \(a_n<-60\), we need \(65-7n<-60\), so \(n>125/7\). The smallest integer satisfying this is \(n=18\). Therefore, \(a_{18}=65-7(18)=-61\). The previous term is \(a_{17}=-54\), which is not less than \(-60\). Although \(-68\) is also less than \(-60\), it occurs later in the AP. Exam tip: when asked for the first term meeting an inequality, use the smallest integer \(n\) that satisfies it.