If Sₙ + Sₙ₋₁ = 12544 and Sₙ − Sₙ₋₁ = 112, what is the value of Sₙ?
Answer and explanation
Correct answer: 6328
Treat the two statements as simultaneous equations. Add them to eliminate Sₙ₋₁: (Sₙ + Sₙ₋₁) + (Sₙ − Sₙ₋₁) = 12544 + 112. The Sₙ₋₁ terms cancel, leaving 2Sₙ = 12656. Dividing by 2 gives Sₙ = 6328, so option C is correct. The result can be checked by finding the other partial sum: Sₙ₋₁ = 12544 − 6328 = 6216. Then 6328 + 6216 = 12544 and 6328 − 6216 = 112, so both original conditions hold. Option A is the value of Sₙ₋₁, a likely distractor. Options B and D arise from an arithmetic or division error and fail the verification.
Frequently asked questions
What is the correct answer to this question?
6328
Why is this the correct answer?
Treat the two statements as simultaneous equations. Add them to eliminate Sₙ₋₁: (Sₙ + Sₙ₋₁) + (Sₙ − Sₙ₋₁) = 12544 + 112. The Sₙ₋₁ terms cancel, leaving 2Sₙ = 12656. Dividing by 2 gives Sₙ = 6328, so option C is correct. The result can be checked by finding the other partial sum: Sₙ₋₁ = 12544 − 6328 = 6216. Then 6328 + 6216 = 12544 and 6328 − 6216 = 112, so both original conditions hold. Option A is the value of Sₙ₋₁, a likely distractor. Options B and D arise from an arithmetic or division error and fail the verification.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Sum of first n natural numbers.
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