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Subjects
Class 10MathematicsArithmetic Progressions (AP)Finding the sum of the first $n$ terms of an APHard
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If (S_n=n(4n+3)), find the sum from the (21)st term to the (35)th term.

Answer and explanation

Correct answer: (3345)

Here the sum of the first n terms is given directly by \\(S_n=n(4n+3)\\). For a range beginning with the 21st term, subtract the sum of the first 20 terms from the sum of the first 35 terms. This leaves exactly terms 21 through 35, including both endpoints.

Calculate \\(S_{35}=35[4(35)+3]=35(140+3)=35(143)=5005\\). Also, \\(S_{20}=20[4(20)+3]=20(80+3)=20(83)=1660\\). Therefore the required sum is \\(S_{35}-S_{20}=5005-1660=3345\\). Hence option D is correct. The subtraction uses 20, not 21, because the 20th term is the last term that must be excluded.

Related tags

Given SnRange SumHard
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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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