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Which formula correctly represents the sum of the first \(n\) terms of an AP with first term \(a\) and common difference \(d\)?
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Answer and explanation
Correct answer: \(\frac{n}{2}[2a+(n-1)d]\)
The \(n\)th term of an AP is \(l=a+(n-1)d\). Hence, \(S_n=\frac{n}{2}(a+l)=\frac{n}{2}[2a+(n-1)d]\). Option B multiplies the last term by \(n\), so it is incorrect. Exam tip: find \(l\) first to check the formula.
Frequently asked questions
What is the correct answer to this question?
\(\frac{n}{2}[2a+(n-1)d]\)
Why is this the correct answer?
The \(n\)th term of an AP is \(l=a+(n-1)d\). Hence, \(S_n=\frac{n}{2}(a+l)=\frac{n}{2}[2a+(n-1)d]\). Option B multiplies the last term by \(n\), so it is incorrect. Exam tip: find \(l\) first to check the formula.
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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