If an arithmetic progression has (S_5=65) and (S_{11}=242), what is the sum of the (6)th to (11)th terms?
Answer and explanation
Correct answer: (177)
The governing concept is the meaning of partial sums in an arithmetic progression. S₁₁ represents the sum of terms 1 through 11, while S₅ represents the sum of terms 1 through 5. Subtracting the latter from the former cancels the first five terms and leaves exactly the sixth through eleventh terms. Therefore, the required sum is S₁₁ − S₅ = 242 − 65 = 177. Hence option B is correct. There is no need to determine the first term or common difference. Options A, C, and D result from incorrect subtraction or from including or excluding the wrong endpoint terms.
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What is the correct answer to this question?
(177)
Why is this the correct answer?
The governing concept is the meaning of partial sums in an arithmetic progression. S₁₁ represents the sum of terms 1 through 11, while S₅ represents the sum of terms 1 through 5. Subtracting the latter from the former cancels the first five terms and leaves exactly the sixth through eleventh terms. Therefore, the required sum is S₁₁ − S₅ = 242 − 65 = 177. Hence option B is correct. There is no need to determine the first term or common difference. Options A, C, and D result from incorrect subtraction or from including or excluding the wrong endpoint terms.
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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