Which is the correct formula for the sum \(S_n\) of the first \(n\) terms of an arithmetic progression with first term \(a\) and common difference \(d\)?
Answer and explanation
Correct answer: \(S_n=\frac{n}{2}[2a+(n-1)d]\)
The \(n\)th term of an AP is \(l=a+(n-1)d\). Therefore, the sum of the first \(n\) terms is \(S_n=\frac{n}{2}(a+l)=\frac{n}{2}[2a+(n-1)d]\). Option B gives only the \(n\)th term, not the sum. Exam tip: ensure that the sum formula contains \((n-1)d\), not \(nd\).
Frequently asked questions
What is the correct answer to this question?
\(S_n=\frac{n}{2}[2a+(n-1)d]\)
Why is this the correct answer?
The \(n\)th term of an AP is \(l=a+(n-1)d\). Therefore, the sum of the first \(n\) terms is \(S_n=\frac{n}{2}(a+l)=\frac{n}{2}[2a+(n-1)d]\). Option B gives only the \(n\)th term, not the sum. Exam tip: ensure that the sum formula contains \((n-1)d\), not \(nd\).
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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