In an AP, the first term is (12), the last term is (72), and total terms are (11). What is the sum?
Answer and explanation
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.
Frequently asked questions
What is the correct answer to this question?
462
Why is this the correct answer?
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.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Arithmetic Progressions (AP). Topic: Finding the sum of the first $n$ terms of an AP.
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