In an AP, the first term is (12), the last term is (72), and total terms are (11). What is the sum?

Correct answer: 462

The sum of the first \(n\) terms of an AP is \(S_n=\frac{n}{2}(a+l)\), where \(a\) is the first term and \(l\) is the last term. Here, \(n=11\), \(a=12\), and \(l=72\). Therefore, \(S_{11}=\frac{11}{2}(12+72)=\frac{11}{2}\times84=462\). Hence, 462 is the correct answer. Although 452 is close, the average of the first and last terms is \(42\), and \(42\times11=462\), not 452. Exam tip: When \(a\), \(l\), and \(n\) are given, apply this sum formula directly.