If the sum of the first (9) terms of an arithmetic progression is (279), and the first term is (7), what is the last term?
Answer and explanation
Correct answer: 55
The sum of the first \(n\) terms of an AP is \(S_n=\frac{n}{2}(a+l)\), where \(l\) is the last term. Therefore, \(279=\frac{9}{2}(7+l)\). This gives \(7+l=62\), so \(l=55\). If the last term were \(53\), the sum would be \(270\), not \(279\). Exam tip: When the first term and the sum are given, use \(S_n=\frac{n}{2}(a+l)\) to find the last term directly.
Frequently asked questions
What is the correct answer to this question?
55
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 \(l\) is the last term. Therefore, \(279=\frac{9}{2}(7+l)\). This gives \(7+l=62\), so \(l=55\). If the last term were \(53\), the sum would be \(270\), not \(279\). Exam tip: When the first term and the sum are given, use \(S_n=\frac{n}{2}(a+l)\) to find the last term 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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