Which of the following statements is correct about the formula for the sum of the first n terms of an arithmetic progression (AP)?
Answer and explanation
Correct answer: If the first term and last term are known, then \(S_n=\frac{n}{2}(a+l)\).
The average of the first and last terms of an AP is \(\frac{a+l}{2}\). Therefore, the sum of the first \(n\) terms is the number of terms multiplied by this average: \(S_n=n\times\frac{a+l}{2}=\frac{n}{2}(a+l)\). Hence, option A is correct. Option C gives only the average of the first and last terms, not the sum. Exam tip: \(l\) denotes the last term, whereas \(d\) denotes the common difference.
Frequently asked questions
What is the correct answer to this question?
If the first term and last term are known, then \(S_n=\frac{n}{2}(a+l)\).
Why is this the correct answer?
The average of the first and last terms of an AP is \(\frac{a+l}{2}\). Therefore, the sum of the first \(n\) terms is the number of terms multiplied by this average: \(S_n=n\times\frac{a+l}{2}=\frac{n}{2}(a+l)\). Hence, option A is correct. Option C gives only the average of the first and last terms, not the sum. Exam tip: \(l\) denotes the last term, whereas \(d\) denotes the common difference.
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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