If an arithmetic progression has S₇ = 126 and S₁₄ = 427, what is the sum of the 8th to 14th terms?
Answer and explanation
Correct answer: 301
The governing concept is the meaning of a partial sum. S₇ represents the sum of the first seven terms, while S₁₄ represents the sum of the first fourteen terms. When the earlier partial sum is subtracted from the later one, the first seven terms cancel, leaving exactly the 8th through 14th terms. Therefore, the required sum is S₁₄ − S₇ = 427 − 126 = 301. Hence option C is correct. The other choices result from an arithmetic error or from subtracting the wrong quantities; no common difference or first term is needed for this direct partial-sum method.
Frequently asked questions
What is the correct answer to this question?
301
Why is this the correct answer?
The governing concept is the meaning of a partial sum. S₇ represents the sum of the first seven terms, while S₁₄ represents the sum of the first fourteen terms. When the earlier partial sum is subtracted from the later one, the first seven terms cancel, leaving exactly the 8th through 14th terms. Therefore, the required sum is S₁₄ − S₇ = 427 − 126 = 301. Hence option C is correct. The other choices result from an arithmetic error or from subtracting the wrong quantities; no common difference or first term is needed for this direct partial-sum method.
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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