What is the sum of the first (50) terms of the AP (2,4,6,\ldots)?

Correct answer: 2550

Here, the first term is \(a=2\), the common difference is \(d=2\), and the number of terms is \(n=50\). Using \(S_n=\frac{n}{2}[2a+(n-1)d]\), we get \(S_{50}=\frac{50}{2}[2\times2+49\times2]=25\times102=2550\). Therefore, 2550 is the correct answer. The value 2500 may result from taking the last term incorrectly instead of \(100\). Exam tip: identify \(a\), \(d\), and \(n\) before substituting into the sum formula.