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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 = 65 and S_11 = 242, what is the sum of the 6th to 11th terms?

Answer and explanation

Correct answer: 177

The governing concept is the meaning of partial sums. S_11 is the sum of terms 1 through 11, whereas S_5 is the sum of terms 1 through 5. Subtracting S_5 from S_11 cancels the common first five terms and leaves exactly terms 6, 7, 8, 9, 10, and 11. Therefore, the required sum is S_11 − S_5 = 242 − 65 = 177. Hence option B is correct. This method is valid for any sequence, and the fact that the sequence is an AP is not needed for this particular subtraction. Options A, C, and D may arise from an arithmetic subtraction error or from accidentally including the fifth term or excluding the eleventh term. No first term or common difference needs to be calculated.

Related tags

Partial SumsAp SumSequence IntervalsArithmetic 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 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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