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Class 10MathematicsArithmetic Progressions (AP)Finding the sum of the first $n$ terms of an APHard
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If (S_n=5n^2-2n), find the sum from the (26)th term to the (40)th term.

Answer and explanation

Correct answer: (4845)

The notation gives the sum of the first n terms as \\(S_n=5n^2-2n\\). To add terms from the 26th through the 40th, use the total through the 40th term and remove the total through the 25th term. This works because the first 25 terms end immediately before the 26th term, so no required term is lost or counted twice.

Calculate \\(S_{40}=5(40)^2-2(40)=8000-80=7920\\). Next, \\(S_{25}=5(25)^2-2(25)=3125-50=3075\\). Therefore the required sum is \\(S_{40}-S_{25}=7920-3075=4845\\). Hence option D follows. Subtracting \\(S_{26}\\) would be wrong because the 26th term must be included.

Related tags

Given SnRange SumAp
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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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