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Class 10MathematicsArithmetic Progressions (AP)Finding the sum of the first $n$ terms of an APEasyLevel 69
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If \(S_n=\frac{n}{2}(a+l)\), \(a=14\), \(l=84\), and \(n=15\), find the sum.

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Answer and explanation

Correct answer: 735

Here \(a=14\), \(l=84\), and \(n=15\). Therefore, \(S_{15}=\frac{15}{2}(14+84)=\frac{15}{2}\times98=15\times49=735\). Hence, 735 is correct. Getting 745 would result from an error in addition or multiplication. Exam tip: add \(a+l\) first and simplify by 2 when the sum is even.

Related tags

Arithmetic ProgressionSum Of ApFirst TermLast TermClass 10 Mathematics

Frequently asked questions

What is the correct answer to this question?

735

Why is this the correct answer?

Here \(a=14\), \(l=84\), and \(n=15\). Therefore, \(S_{15}=\frac{15}{2}(14+84)=\frac{15}{2}\times98=15\times49=735\). Hence, 735 is correct. Getting 745 would result from an error in addition or multiplication. Exam tip: add \(a+l\) first and simplify by 2 when the sum is even.

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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