If Sₙ + Sₙ₋₁ = 5625 and Sₙ − Sₙ₋₁ = 75, what is the value of Sₙ?
Answer and explanation
Correct answer: 2850
This is a simultaneous-equation problem involving two consecutive partial sums. Add the equations so that Sₙ₋₁ is eliminated: (Sₙ + Sₙ₋₁) + (Sₙ − Sₙ₋₁) = 5625 + 75. The middle terms cancel, giving 2Sₙ = 5700. Dividing both sides by 2 gives Sₙ = 2850, so option B is correct. Substitution verifies the result: if Sₙ = 2850, then Sₙ₋₁ = 5625 − 2850 = 2775, and 2850 − 2775 = 75. Option A is the corresponding previous partial sum, which is a plausible result of stopping after elimination. Options C and D do not satisfy both given equations, so they are not valid values of Sₙ.
Frequently asked questions
What is the correct answer to this question?
2850
Why is this the correct answer?
This is a simultaneous-equation problem involving two consecutive partial sums. Add the equations so that Sₙ₋₁ is eliminated: (Sₙ + Sₙ₋₁) + (Sₙ − Sₙ₋₁) = 5625 + 75. The middle terms cancel, giving 2Sₙ = 5700. Dividing both sides by 2 gives Sₙ = 2850, so option B is correct. Substitution verifies the result: if Sₙ = 2850, then Sₙ₋₁ = 5625 − 2850 = 2775, and 2850 − 2775 = 75. Option A is the corresponding previous partial sum, which is a plausible result of stopping after elimination. Options C and D do not satisfy both given equations, so they are not valid values of Sₙ.
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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