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Class 10MathematicsArithmetic Progressions (AP)Finding the sum of the first $n$ terms of an APMediumLevel 68
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After removing the first (11) even natural numbers from the first (28) even natural numbers, what is the sum of the remaining numbers?

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Answer and explanation

Correct answer: 680

The sum of the first 28 even natural numbers is \(28(28+1)=812\). The sum of the first 11 even natural numbers is \(11(11+1)=132\). Therefore, the sum of the remaining numbers is \(812-132=680\). A value such as 660 can result from an error in counting terms or subtraction. Exam tip: the sum of the first \(n\) even natural numbers is \(n(n+1)\).

Related tags

Arithmetic ProgressionEven Natural NumbersSum Of TermsPartial SumsClass 10 Mathematics

Frequently asked questions

What is the correct answer to this question?

680

Why is this the correct answer?

The sum of the first 28 even natural numbers is \(28(28+1)=812\). The sum of the first 11 even natural numbers is \(11(11+1)=132\). Therefore, the sum of the remaining numbers is \(812-132=680\). A value such as 660 can result from an error in counting terms or subtraction. Exam tip: the sum of the first \(n\) even natural numbers is \(n(n+1)\).

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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