What is the first term greater than (200) in the AP (2,9,16,\ldots)?

205

Here, the first term is \(a=2\) and the common difference is \(d=7\). Thus, the \(n\)th term is \(a_n=2+7(n-1)=7n-5\). From \(7n-5>200\), we get \(n>\frac{205}{7}\), so the smallest integer value is \(n=30\). Therefore, \(a_{30}=205\), making 205 the first term greater than 200. Although 198 is the nearest preceding term, it is not greater than 200. Exam tip: for the first term greater than a given number, solve the inequality and take the smallest valid integer value of \(n\).

This is a Class 10 Mathematics question. Chapter: Arithmetic Progressions (AP). Topic: Finding the $n$th term of an AP.