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Class 10MathematicsArithmetic Progressions (AP)Finding the sum of the first $n$ terms of an APEasy
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What is the sum of the first (25) terms of the AP (14,18,22,\ldots)?

Answer and explanation

Correct answer: 1550

Here, the first term is \(a=14\), the common difference is \(d=18-14=4\), and the number of terms is \(n=25\). The 25th term is \(a_{25}=a+(n-1)d=14+24\times4=110\). Hence, \(S_{25}=\frac{n}{2}(a+l)=\frac{25}{2}(14+110)=1550\). Therefore, 1550 is the correct answer. A close option such as 1575 may result from an error in finding the last term or the number of terms. Exam tip: always check the \(n-1\) factor while finding the last term.

Related tags

Arithmetic ProgressionAp SumSum Of First N TermsClass 10 MathematicsSequences And SeriesFinding 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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