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Class 10MathematicsArithmetic Progressions (AP)Finding the sum of the first $n$ terms of an APMediumLevel 52
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What is the sum of the first 12 terms of the arithmetic progression (5, 9, 13, 17, …)?

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Answer and explanation

Correct answer: 324

The governing concept is the sum formula for the first n terms of an arithmetic progression: Sₙ = n/2[2a + (n − 1)d]. Here n = 12, a = 5, and d = 9 − 5 = 4. Therefore S₁₂ = 12/2[2(5) + 11(4)] = 6[10 + 44] = 6 × 54 = 324. Thus option B is correct. A common alternative check is to find the last term: a₁₂ = 5 + 11 × 4 = 49, then use S₁₂ = 12(5 + 49)/2 = 324. The other choices result from arithmetic errors in the bracket or from using the wrong number of intervals rather than the number of terms.

Related tags

Arithmetic-ProgressionSum-Of-TermsSequencesClass-9Finding The Sum Of The First $N$ Terms Of An ApFinding The Sum Of The First N Terms Of An ApArithmetic Progressions (Ap)Arithmetic Progressions Ap

Frequently asked questions

What is the correct answer to this question?

324

Why is this the correct answer?

The governing concept is the sum formula for the first n terms of an arithmetic progression: Sₙ = n/2[2a + (n − 1)d]. Here n = 12, a = 5, and d = 9 − 5 = 4. Therefore S₁₂ = 12/2[2(5) + 11(4)] = 6[10 + 44] = 6 × 54 = 324. Thus option B is correct. A common alternative check is to find the last term: a₁₂ = 5 + 11 × 4 = 49, then use S₁₂ = 12(5 + 49)/2 = 324. The other choices result from arithmetic errors in the bracket or from using the wrong number of intervals rather than the number of terms.

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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