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Class 10MathematicsArithmetic Progressions (AP)Finding the sum of the first $n$ terms of an APEasyLevel 69
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Find the sum of the first (8) terms of the arithmetic progression (40,36,32,\ldots).

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Answer and explanation

Correct answer: (208)

The governing concept is the sum of the first n terms of an arithmetic progression. Here the first term is a = 40 and the common difference is d = 36 − 40 = −4. The eighth term is a₈ = a + 7d = 40 + 7(−4) = 12. Now use S₈ = n(a + l) ÷ 2: S₈ = 8(40 + 12) ÷ 2 = 4 × 52 = 208. Therefore, option A is correct. The negative common difference must be retained because the progression is decreasing. The other options reflect an incorrect final term or an arithmetic mistake.

Related tags

Arithmetic ProgressionAp SumDecreasing ProgressionFinding The Sum Of The First $N$ Terms Of An ApFinding The Sum Of The First N Terms Of An ApArithmetic Progressions (Ap)Arithmetic Progressions ApMathematics

Frequently asked questions

What is the correct answer to this question?

(208)

Why is this the correct answer?

The governing concept is the sum of the first n terms of an arithmetic progression. Here the first term is a = 40 and the common difference is d = 36 − 40 = −4. The eighth term is a₈ = a + 7d = 40 + 7(−4) = 12. Now use S₈ = n(a + l) ÷ 2: S₈ = 8(40 + 12) ÷ 2 = 4 × 52 = 208. Therefore, option A is correct. The negative common difference must be retained because the progression is decreasing. The other options reflect an incorrect final term or an arithmetic mistake.

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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