If the AP is (9,13,17,\ldots), what is the sum of the first (11) terms?

319

Here, the first term is \(a=9\), the common difference is \(d=13-9=4\), and \(n=11\). Using \(S_n=\frac{n}{2}[2a+(n-1)d]\), we get \(S_{11}=\frac{11}{2}[2(9)+10(4)]=\frac{11}{2}\times58=319\). Therefore, option A is correct. A nearby value such as option B may result from using an incorrect value for \((n-1)d\) or making a multiplication error. Exam tip: identify \(a\), \(d\), and \(n\) separately before applying the formula.

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