In the AP (-68,-49,-30,\ldots), what is the first term greater than (700)?

Correct answer: 711

Here, the first term is \(a=-68\) and the common difference is \(d=19\). Thus, \(a_n=-68+19(n-1)\). For \(a_n>700\), \(-68+19(n-1)>700\), giving \(n>41.42\). The smallest integer value is \(n=42\). Therefore, \(a_{42}=711\), so 711 is the first term greater than 700. Although 692 is the nearest preceding term, it is less than 700. Exam tip: for the “first term greater than” condition, solve the inequality and take the smallest valid integer \(n\).