If an arithmetic progression has first term \(a\), last term \(l\), and \(n\) terms, which is the correct formula for the sum \(S_n\) of its first \(n\) terms?
Answer and explanation
Correct answer: \(S_n=\frac{n}{2}(a+l)\)
The sum of the first \(n\) terms of an AP equals the number of terms multiplied by the average of the first and last terms. Thus, \(S_n=n\times\frac{a+l}{2}=\frac{n}{2}(a+l)\). Option C is the formula for the \(n\)th term, while option D gives only the average of the first and last terms. Exam tip: use this form when the last term \(l\) is known.
Frequently asked questions
What is the correct answer to this question?
\(S_n=\frac{n}{2}(a+l)\)
Why is this the correct answer?
The sum of the first \(n\) terms of an AP equals the number of terms multiplied by the average of the first and last terms. Thus, \(S_n=n\times\frac{a+l}{2}=\frac{n}{2}(a+l)\). Option C is the formula for the \(n\)th term, while option D gives only the average of the first and last terms. Exam tip: use this form when the last term \(l\) is known.
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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