If the first term, last term, and number of terms of an arithmetic progression are known, which formula is appropriate for finding the sum of its first \(n\) terms?
Answer and explanation
Correct answer: \(S_n=\frac{n}{2}(a+l)\)
For an AP with first term \(a\), last term \(l\), and \(n\) terms, the sum is \(S_n=\frac{n}{2}(a+l)\). It equals the number of terms multiplied by the average of the first and last terms, \(\frac{a+l}{2}\). Option D is also a valid general sum formula, but it is used when the common difference \(d\), rather than the last term \(l\), is known. Exam tip: use \(\frac{n}{2}(a+l)\) directly when \(l\) is given.
Frequently asked questions
What is the correct answer to this question?
\(S_n=\frac{n}{2}(a+l)\)
Why is this the correct answer?
For an AP with first term \(a\), last term \(l\), and \(n\) terms, the sum is \(S_n=\frac{n}{2}(a+l)\). It equals the number of terms multiplied by the average of the first and last terms, \(\frac{a+l}{2}\). Option D is also a valid general sum formula, but it is used when the common difference \(d\), rather than the last term \(l\), is known. Exam tip: use \(\frac{n}{2}(a+l)\) directly when \(l\) is given.
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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