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Class 10MathematicsArithmetic Progressions (AP)Finding the sum of the first $n$ terms of an APHardLevel 67
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In the AP (50, 47, 44, ...), what is the sum of the terms from the 6th term to the 20th term, inclusive?

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Answer and explanation

Correct answer: 210

The governing concept is the sum of a consecutive block of terms of an arithmetic progression. Here the first term is a = 50 and the common difference is d = -3. The 6th term is a6 = 50 + 5(-3) = 35, and the 20th term is a20 = 50 + 19(-3) = -7. There are 20 - 6 + 1 = 15 terms in the required block. Using the AP sum formula, block sum = 15/2 × (35 + (-7)) = 15/2 × 28 = 210. Thus option C is correct. A and B are smaller incorrect totals, while D does not follow from the two endpoint terms and the correct number of terms.

Related tags

Arithmetic ProgressionConsecutive TermsAp 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 Ap

Frequently asked questions

What is the correct answer to this question?

210

Why is this the correct answer?

The governing concept is the sum of a consecutive block of terms of an arithmetic progression. Here the first term is a = 50 and the common difference is d = -3. The 6th term is a6 = 50 + 5(-3) = 35, and the 20th term is a20 = 50 + 19(-3) = -7. There are 20 - 6 + 1 = 15 terms in the required block. Using the AP sum formula, block sum = 15/2 × (35 + (-7)) = 15/2 × 28 = 210. Thus option C is correct. A and B are smaller incorrect totals, while D does not follow from the two endpoint terms and the correct 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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