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Class 10MathematicsArithmetic Progressions (AP)Finding the sum of the first $n$ terms of an APHardLevel 69
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If an arithmetic progression has first term \(a\) and common difference \(d\), which of the following expressions represents the sum \(S_n\) of its first \(n\) terms?

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Answer and explanation

Correct answer: \(S_n=\frac{n}{2}[2a+(n-1)d]\)

The sum of the first \(n\) AP terms is \(S_n=\frac{n}{2}[2a+(n-1)d]\). Option B gives the \(n\)th term \(a_n\), not the sum. In exams, carefully check the \(n-1\) factor.

Related tags

Arithmetic ProgressionAp SumSum Of N TermsSequence FormulasClass 10 Mathematics

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 sum of the first \(n\) AP terms is \(S_n=\frac{n}{2}[2a+(n-1)d]\). Option B gives the \(n\)th term \(a_n\), not the sum. In exams, carefully check the \(n-1\) factor.

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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10 more MCQs
  1. 1If an arithmetic progression has first term \(a\), common difference \(d\), and \(n\) terms, which formula correctly represents the sum of its first \(n\) terms?
  2. 2Find the sum of the first (15) terms of the AP (4,8,12,\ldots).
  3. 3Which formula correctly represents the sum of the first \(n\) terms of an AP with first term \(a\) and common difference \(d\)?
  4. 4What is the sum of the first (25) terms of the AP (1,3,5,\ldots)?
  5. 5What is the sum of the first (12) terms of the AP (10,20,30,\ldots)?
  6. 6What will be the sum of the first (10) terms of the AP (7,14,21,\ldots)?
  7. 7If the first term of an AP is (5), the last term is (45), and the number of terms is (9), what is the sum?
  8. 8Find the sum of the first (30) terms of the AP (3,6,9,\ldots).
  9. 9What is the sum of the first (8) terms of the AP (20,18,16,\ldots)?
  10. 10If the AP is (9,13,17,\ldots), what is the sum of the first (11) terms?
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