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Class 10MathematicsArithmetic Progressions (AP)Finding the sum of the first $n$ terms of an APMediumLevel 69
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If (S_n=5n^2-n), what is the value of (S_9)?

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Answer and explanation

Correct answer: 396

Given \(S_n=5n^2-n\), substitute \(n=9\): \(S_9=5(9)^2-9=5\times81-9=405-9=396\). Hence, 396 is the correct option. 405 is only \(5\times81\); the final subtraction of 9 must also be done. Exam tip: after substituting \(n\), evaluate the power first, then multiply and subtract.

Related tags

Arithmetic ProgressionSum Of N TermsSubstitutionQuadratic ExpressionClass 10 Mathematics

Frequently asked questions

What is the correct answer to this question?

396

Why is this the correct answer?

Given \(S_n=5n^2-n\), substitute \(n=9\): \(S_9=5(9)^2-9=5\times81-9=405-9=396\). Hence, 396 is the correct option. 405 is only \(5\times81\); the final subtraction of 9 must also be done. Exam tip: after substituting \(n\), evaluate the power first, then multiply and subtract.

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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