If the first term of an arithmetic progression is (11), the last term is (71), and the number of terms is (16), what is the sum?
Answer and explanation
Correct answer: 656
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. Thus, \(S_{16}=\frac{16}{2}(11+71)=8\times82=656\). Therefore, 656 is correct. The value 646 would result from an arithmetic error in addition or multiplication. Exam tip: When the first and last terms are given, use \(\frac{n}{2}(a+l)\) directly.
Frequently asked questions
What is the correct answer to this question?
656
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. Thus, \(S_{16}=\frac{16}{2}(11+71)=8\times82=656\). Therefore, 656 is correct. The value 646 would result from an arithmetic error in addition or multiplication. Exam tip: When the first and last terms are given, use \(\frac{n}{2}(a+l)\) 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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