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Class 10MathematicsArithmetic Progressions (AP)Finding the sum of the first $n$ terms of an APMediumLevel 69
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The lengths of rods in a ladder are (40,43,46,\ldots) cm. What is the total length of the first (15) rods?

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Answer and explanation

Correct answer: 915 cm

This is an AP with first term \(a=40\), common difference \(d=3\), and \(n=15\) terms. Using \(S_n=\frac{n}{2}[2a+(n-1)d]\), \(S_{15}=\frac{15}{2}[2(40)+14(3)]=\frac{15}{2}(122)=915\) cm. Hence, the correct answer is 915 cm. An option such as 900 cm may result from using the common difference or last term incorrectly. Exam tip: always use \(n-1\) in the AP sum formula.

Related tags

Arithmetic ProgressionAp SumSum Of N TermsMathematicsClass 10

Frequently asked questions

What is the correct answer to this question?

915 cm

Why is this the correct answer?

This is an AP with first term \(a=40\), common difference \(d=3\), and \(n=15\) terms. Using \(S_n=\frac{n}{2}[2a+(n-1)d]\), \(S_{15}=\frac{15}{2}[2(40)+14(3)]=\frac{15}{2}(122)=915\) cm. Hence, the correct answer is 915 cm. An option such as 900 cm may result from using the common difference or last term incorrectly. Exam tip: always use \(n-1\) in the AP 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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