If an arithmetic progression has first term \(a\), last term \(l\), and \(n\) terms, which is the correct formula for the sum of its first \(n\) terms?
Answer and explanation
Correct answer: \(\frac{n}{2}(a+l)\)
The sum of the first \(n\) terms of an AP is the number of terms multiplied by the average of the first and last terms. Hence, \(S_n=n\times\frac{a+l}{2}=\frac{n}{2}(a+l)\). Option B does not divide by \(2\), while option C gives only the average of the first and last terms, not the sum. Exam tip: use this formula directly when the last term \(l\) is known.
Frequently asked questions
What is the correct answer to this question?
\(\frac{n}{2}(a+l)\)
Why is this the correct answer?
The sum of the first \(n\) terms of an AP is the number of terms multiplied by the average of the first and last terms. Hence, \(S_n=n\times\frac{a+l}{2}=\frac{n}{2}(a+l)\). Option B does not divide by \(2\), while option C gives only the average of the first and last terms, not the sum. 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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