If in an AP S₂₂ = 1474 and S₁₁ = 407, what is the sum from the 12th term to the 22nd term?
Answer and explanation
Correct answer: 1067
S₂₂ represents the sum of the first 22 terms, while S₁₁ represents the sum of the first 11 terms. Removing the first 11 terms from the first 22 terms leaves exactly the 12th through 22nd terms, inclusive. Therefore the required sum is S₂₂ − S₁₁ = 1474 − 407 = 1067. There are 11 terms in this range, but it is not necessary to find the first term or common difference because the two given partial sums already provide the required subtraction directly. Hence option C, 1067, is correct. The other options result from addition, an incorrect subtraction, or a small arithmetic error.
Frequently asked questions
What is the correct answer to this question?
1067
Why is this the correct answer?
S₂₂ represents the sum of the first 22 terms, while S₁₁ represents the sum of the first 11 terms. Removing the first 11 terms from the first 22 terms leaves exactly the 12th through 22nd terms, inclusive. Therefore the required sum is S₂₂ − S₁₁ = 1474 − 407 = 1067. There are 11 terms in this range, but it is not necessary to find the first term or common difference because the two given partial sums already provide the required subtraction directly. Hence option C, 1067, is correct. The other options result from addition, an incorrect subtraction, or a small arithmetic error.
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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