If in an AP, S₁₆ = 880 and S₈ = 280, what is the sum from the 9th term to the 16th term?
Answer and explanation
Correct answer: 600
The governing idea is that a partial sum S_k contains the first k terms. Therefore, subtracting S₈ from S₁₆ removes the first eight terms and leaves exactly the terms from the 9th through the 16th. Thus, required sum = S₁₆ − S₈ = 880 − 280 = 600. Hence option A is correct. This method avoids finding the first term or common difference separately. A common mistake is to use S₁₆ + S₈, which would count the first eight terms again, or to subtract in the reverse order and obtain a negative value. Options B, C, and D do not equal the correct difference.
Frequently asked questions
What is the correct answer to this question?
600
Why is this the correct answer?
The governing idea is that a partial sum S_k contains the first k terms. Therefore, subtracting S₈ from S₁₆ removes the first eight terms and leaves exactly the terms from the 9th through the 16th. Thus, required sum = S₁₆ − S₈ = 880 − 280 = 600. Hence option A is correct. This method avoids finding the first term or common difference separately. A common mistake is to use S₁₆ + S₈, which would count the first eight terms again, or to subtract in the reverse order and obtain a negative value. Options B, C, and D do not equal the correct difference.
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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