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Class 10MathematicsArithmetic Progressions (AP)Finding the sum of the first $n$ terms of an APHard
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If the sum of an AP is (S_n=7n^2-4n), find the sum from the (21)st term to the (30)th term.

Answer and explanation

Correct answer: (3460)

When a question gives the sum of the first n terms, the sum of any consecutive block can be found by subtracting the sum before that block. The terms from the 21st through the 30th are obtained by removing the first 20 terms from the first 30 terms. Thus the required expression is \\(S_{30}-S_{20}\\), not \\(S_{30}-S_{21}\\), because the 21st term must be included.

Using \\(S_n=7n^2-4n\\), we get \\(S_{30}=7(30)^2-4(30)=6180\\) and \\(S_{20}=7(20)^2-4(20)=2720\\). Therefore, the required sum is \\(6180-2720=3460\\). Option A is correct. A common mistake is to subtract \\(S_{21}\\), which would leave out the 21st term.

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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