Find the sum of the first (14) terms of the arithmetic progression (6,9,12,\ldots).

Correct answer: 357

Here, the first term is \(a=6\), the common difference is \(d=9-6=3\), and the number of terms is \(n=14\). Using \(S_n=\frac{n}{2}[2a+(n-1)d]\), we get \(S_{14}=\frac{14}{2}[2(6)+13(3)]=7(51)=357\). Hence, 357 is correct. An option such as 367 usually results from an error while calculating \((n-1)d\) or adding the terms. Exam tip: write down \(a\), \(d\), and \(n\) separately before applying the sum formula.