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Class 10MathematicsArithmetic Progressions (AP)Finding the sum of the first $n$ terms of an APEasy
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Find the sum of the first (15) terms of the AP (4,8,12,\ldots).

Answer and explanation

Correct answer: 480

Here, the first term is \(a=4\), the common difference is \(d=4\), and \(n=15\). Using \(S_n=\frac{n}{2}[2a+(n-1)d]\), we get \(S_{15}=\frac{15}{2}[2(4)+14(4)]=\frac{15}{2}(64)=480\). Therefore, 480 is correct. A value such as 420 can result from using the wrong number of terms or last term. Exam tip: write down \(a\), \(d\), and \(n\) before applying the AP sum formula.

Related tags

Arithmetic ProgressionAp SumSum Of N TermsClass 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. 2Which formula correctly represents the sum of the first \(n\) terms of an AP with first term \(a\) and common difference \(d\)?
  3. 3What is the sum of the first (25) terms of the AP (1,3,5,\ldots)?
  4. 4What is the sum of the first (12) terms of the AP (10,20,30,\ldots)?
  5. 5What will be the sum of the first (10) terms of the AP (7,14,21,\ldots)?
  6. 6If the first term of an AP is (5), the last term is (45), and the number of terms is (9), what is the sum?
  7. 7Find the sum of the first (30) terms of the AP (3,6,9,\ldots).
  8. 8What is the sum of the first (8) terms of the AP (20,18,16,\ldots)?
  9. 9If the AP is (9,13,17,\ldots), what is the sum of the first (11) terms?
  10. 10What is the sum of the first (14) terms of the AP (12,17,22,\ldots)?
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