If Sₙ − Sₙ₋₁ = 68, what will be Sₙ?
Answer and explanation
Correct answer: 2346
Let Sₙ denote 1 + 2 + 3 + ⋯ + n, the sum of the first n natural numbers. The governing property is Sₙ − Sₙ₋₁ = n, because subtracting the sum through n − 1 leaves only the last term n. Therefore the given difference 68 tells us that n = 68. We then calculate S₆₈ using Sₙ = n(n + 1)/2: S₆₈ = 68 × 69/2 = 34 × 69 = 2346. Thus option B is correct. Option A is smaller than the required sum and can arise from an arithmetic error; option C equals S₆₉, while option D does not follow the formula. The difference identifies the index, and the formula gives the requested total.
Frequently asked questions
What is the correct answer to this question?
2346
Why is this the correct answer?
Let Sₙ denote 1 + 2 + 3 + ⋯ + n, the sum of the first n natural numbers. The governing property is Sₙ − Sₙ₋₁ = n, because subtracting the sum through n − 1 leaves only the last term n. Therefore the given difference 68 tells us that n = 68. We then calculate S₆₈ using Sₙ = n(n + 1)/2: S₆₈ = 68 × 69/2 = 34 × 69 = 2346. Thus option B is correct. Option A is smaller than the required sum and can arise from an arithmetic error; option C equals S₆₉, while option D does not follow the formula. The difference identifies the index, and the formula gives the requested total.
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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