If in an AP, S₅ = 75 and S₁₀ = 275, what is the value of S₂₀?
Answer and explanation
Correct answer: 1050
The governing concept is the sum of the first n terms of an arithmetic progression: Sₙ = n/2[2a + (n−1)d]. Using S₅ = 75 gives 5/2(2a + 4d) = 75, so a + 2d = 15. Using S₁₀ = 275 gives 10/2(2a + 9d) = 275, so 2a + 9d = 55. Since 2a + 4d = 30, subtraction gives 5d = 25, hence d = 5 and a = 5. Therefore S₂₀ = 20/2[2(5) + 19(5)] = 10(105) = 1050. Thus option C is correct. Options A, B, and D result from using an incorrect common difference or an incorrect sum formula.
Frequently asked questions
What is the correct answer to this question?
1050
Why is this the correct answer?
The governing concept is the sum of the first n terms of an arithmetic progression: Sₙ = n/2[2a + (n−1)d]. Using S₅ = 75 gives 5/2(2a + 4d) = 75, so a + 2d = 15. Using S₁₀ = 275 gives 10/2(2a + 9d) = 275, so 2a + 9d = 55. Since 2a + 4d = 30, subtraction gives 5d = 25, hence d = 5 and a = 5. Therefore S₂₀ = 20/2[2(5) + 19(5)] = 10(105) = 1050. Thus option C is correct. Options A, B, and D result from using an incorrect common difference or an incorrect 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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