If the first term \(a\), last term \(l\), and total number of terms \(n\) of an arithmetic progression are known, which formula is directly used to find the sum of the 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, \(S_n=n\times\frac{a+l}{2}=\frac{n}{2}(a+l)\). Therefore, option B is correct. Option A misses division by 2, while option C gives only the average of the first and last terms. Exam tip: use this formula directly 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, \(S_n=n\times\frac{a+l}{2}=\frac{n}{2}(a+l)\). Therefore, option B is correct. Option A misses division by 2, while option C gives only the average of the first and last terms. Exam tip: use this formula directly 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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