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Class 10MathematicsArithmetic Progressions (AP)Finding the sum of the first $n$ terms of an APEasyLevel 69
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What is the sum of the first (18) terms of the arithmetic progression (1,6,11,\ldots)?

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Answer and explanation

Correct answer: (783)

The governing concept is the sum formula for an arithmetic progression. The first term is a = 1 and the common difference is d = 6 − 1 = 5. The eighteenth term is a₁₈ = a + 17d = 1 + 17 × 5 = 86. Therefore, S₁₈ = n(a + l) ÷ 2 = 18(1 + 86) ÷ 2 = 9 × 87 = 783. Thus option B is correct. The factor 17 is used because the eighteenth term is reached through 18 − 1 intervals. The other choices usually result from using 18 differences, miscomputing the last term, or making an arithmetic error.

Related tags

Arithmetic ProgressionAp SumCommon DifferenceFinding The Sum Of The First $N$ Terms Of An ApFinding The Sum Of The First N Terms Of An ApArithmetic Progressions (Ap)Arithmetic Progressions ApMathematics

Frequently asked questions

What is the correct answer to this question?

(783)

Why is this the correct answer?

The governing concept is the sum formula for an arithmetic progression. The first term is a = 1 and the common difference is d = 6 − 1 = 5. The eighteenth term is a₁₈ = a + 17d = 1 + 17 × 5 = 86. Therefore, S₁₈ = n(a + l) ÷ 2 = 18(1 + 86) ÷ 2 = 9 × 87 = 783. Thus option B is correct. The factor 17 is used because the eighteenth term is reached through 18 − 1 intervals. The other choices usually result from using 18 differences, miscomputing the last term, or making an arithmetic error.

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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