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If an arithmetic progression has first term \(a\) and \(n\)th term \(l\), which is the correct formula for the sum of its first \(n\) terms?
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Answer and explanation
Correct answer: \(\frac{n}{2}(a+l)\)
In an AP, the average of the first and last terms is \(\frac{a+l}{2}\). Multiplying this by the number of terms \(n\) gives \(S_n=\frac{n}{2}(a+l)\). Option B is only the average, not the sum. In exams, use this form when \(l\) is given.
Frequently asked questions
What is the correct answer to this question?
\(\frac{n}{2}(a+l)\)
Why is this the correct answer?
In an AP, the average of the first and last terms is \(\frac{a+l}{2}\). Multiplying this by the number of terms \(n\) gives \(S_n=\frac{n}{2}(a+l)\). Option B is only the average, not the sum. In exams, use this form when \(l\) is given.
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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