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Class 10MathematicsArithmetic Progressions (AP)Finding the sum of the first $n$ terms of an APHardLevel 67
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If an arithmetic progression has a non-zero common difference, what is the nature of the sum \(S_n\) of its first \(n\) terms as a function of \(n\)?

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Answer and explanation

Correct answer: Quadratic function

In \(S_n=\frac{n}{2}[2a+(n-1)d]\), the coefficient of \(n^2\) is \(\frac d2\). Since \(d\ne0\), \(S_n\) is quadratic, not linear. Exam tip: check the \(n^2\) term first.

Related tags

Arithmetic ProgressionSum Of N TermsQuadratic FunctionCommon DifferenceClass 10 Mathematics

Frequently asked questions

What is the correct answer to this question?

Quadratic function

Why is this the correct answer?

In \(S_n=\frac{n}{2}[2a+(n-1)d]\), the coefficient of \(n^2\) is \(\frac d2\). Since \(d\ne0\), \(S_n\) is quadratic, not linear. Exam tip: check the \(n^2\) term first.

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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