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Class 10MathematicsArithmetic Progressions (AP)Finding the sum of the first $n$ terms of an APEasyLevel 67
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What is the sum of the first (14) terms of the AP (8,16,24,\ldots)?

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Answer and explanation

Correct answer: 840

Here, \(a=8\), \(d=8\), and \(n=14\). The 14th term is \(a_{14}=a+(n-1)d=8+13\times8=112\). Hence, \(S_{14}=\frac{14}{2}(8+112)=7\times120=840\). Therefore, 840 is the correct answer. While \(14\times8=112\) gives the 14th term, it does not give the sum. Exam tip: Use both the first and last terms in the sum formula.

Related tags

Arithmetic ProgressionAp SumSum Of First N TermsClass 10 MathematicsCommon Difference

Frequently asked questions

What is the correct answer to this question?

840

Why is this the correct answer?

Here, \(a=8\), \(d=8\), and \(n=14\). The 14th term is \(a_{14}=a+(n-1)d=8+13\times8=112\). Hence, \(S_{14}=\frac{14}{2}(8+112)=7\times120=840\). Therefore, 840 is the correct answer. While \(14\times8=112\) gives the 14th term, it does not give the sum. Exam tip: Use both the first and last terms in the sum formula.

Which subject and chapter does this question cover?

This is a Class 10 Mathematics question. Chapter: Arithmetic Progressions (AP). Topic: Finding the sum of the first $n$ terms of an 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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