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Class 10MathematicsArithmetic Progressions (AP)Finding the sum of the first $n$ terms of an APEasy
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If an arithmetic progression has (S_5=50) and (S_{10}=175), what is the sum of the (6)th to (10)th terms?

Answer and explanation

Correct answer: 125

The sum of the first 10 terms is \(S_{10}=175\), while the sum of the first 5 terms is \(S_5=50\). Hence, the sum from the 6th to the 10th term is \(S_{10}-S_5=175-50=125\). Subtracting \(S_5\) removes exactly the first five terms; 120 does not follow from the correct partial-sum relation. Exam tip: To find the sum of consecutive terms, subtract the smaller partial sum from the larger partial sum.

Related tags

Arithmetic ProgressionPartial SumsSum Of TermsClass 10 MathematicsApFinding The Sum Of The First $N$ Terms Of An ApFinding The Sum Of The First N Terms Of An ApArithmetic Progressions (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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