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Class 10MathematicsArithmetic Progressions (AP)Finding the sum of the first $n$ terms of an APEasyLevel 67
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If an arithmetic progression has S₁₀ = 270 and S₅ = 85, what is the sum of the 6th to 10th terms?

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Answer and explanation

Correct answer: 185

Let Sₙ denote the sum of the first n terms of the arithmetic progression. The sum of terms from the 6th through the 10th is obtained by removing the sum of the first five terms from the sum of the first ten terms. Thus, a₆ + a₇ + a₈ + a₉ + a₁₀ = S₁₀ − S₅ = 270 − 85 = 185. Therefore option C is correct. No separate calculation of the first or last term is needed. Options A, B, and D result from an incorrect subtraction or from confusing the requested five terms with another partial sum.

Related tags

Ap SumPartial SumsArithmetic ProgressionFinding 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?

185

Why is this the correct answer?

Let Sₙ denote the sum of the first n terms of the arithmetic progression. The sum of terms from the 6th through the 10th is obtained by removing the sum of the first five terms from the sum of the first ten terms. Thus, a₆ + a₇ + a₈ + a₉ + a₁₀ = S₁₀ − S₅ = 270 − 85 = 185. Therefore option C is correct. No separate calculation of the first or last term is needed. Options A, B, and D result from an incorrect subtraction or from confusing the requested five terms with another partial sum.

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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