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Class 10MathematicsArithmetic Progressions (AP)Finding the sum of the first $n$ terms of an APMedium
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If (S_{10}=250) and (S_9=207), what is the (10)th term?

Answer and explanation

Correct answer: 43

In an AP, the difference between the sums of the first n and first \(n-1\) terms gives the nth term: \(a_n=S_n-S_{n-1}\). Thus, \(a_{10}=S_{10}-S_9=250-207=43\). Therefore, 43 is correct. Getting 42 would mean subtracting the given sums incorrectly. Exam tip: When two consecutive partial sums are given, subtract them directly to obtain the corresponding term.

Related tags

Arithmetic ProgressionPartial SumsNth TermClass 10 MathematicsFinding 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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