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Subjects
Class 10MathematicsArithmetic Progressions (AP)Finding the sum of the first $n$ terms of an APHard
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In an AP, the sum of the first 15 terms equals the sum of the first 21 terms, i.e., \(S_{15}=S_{21}\). If the first term is \(a\) and the common difference is \(d\), which of the following relation must be true?

Answer and explanation

Correct answer: \(2a+35d=0\)

From \(S_{15}=S_{21}\), the sum of the 16th to 21st terms is zero. Their sum is \(3[(a+15d)+(a+20d)]\), giving \(2a+35d=0\). Exam tip: subtract equal partial sums to isolate the intervening terms.

Related tags

Arithmetic ProgressionAp SumsPartial SumsCommon DifferenceAlgebraic ConditionFinding 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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