In the AP (260,245,230,\ldots), which is the first term less than (-100)?

Correct answer: (-115)

In this AP, the first term is 260 and the common difference is \(d=-15\). \((-100)\) is itself a term of the AP, since \(260-15\times 24=-100\). As each successive term decreases by 15, the term after \((-100)\) is \((-100)-15=-115\). Therefore, the first term less than \((-100)\) is \((-115)\). Although \((-130)\) is also less than \((-100)\), it occurs later. Exam tip: when asked for the “first” term beyond a boundary, check the term immediately after the boundary term.