What is obtained by subtracting the sum of the first 60 natural numbers from the sum of the first 64 natural numbers?
Answer and explanation
Correct answer: 250
The governing concept is the sum of the first n natural numbers and cancellation of common terms. Let Sₙ = 1 + 2 + ... + n. In S₆₄ − S₆₀, the terms 1 through 60 occur in both sums and cancel, leaving 61 + 62 + 63 + 64. Pairing the remaining terms gives (61 + 64) + (62 + 63) = 125 + 125 = 250. The standard formula confirms this: S₆₄ = 64×65/2 = 2080 and S₆₀ = 60×61/2 = 1830, so their difference is 2080 − 1830 = 250. Hence option C is correct. The other options can result from omitting a remaining term or making an arithmetic error.
Frequently asked questions
What is the correct answer to this question?
250
Why is this the correct answer?
The governing concept is the sum of the first n natural numbers and cancellation of common terms. Let Sₙ = 1 + 2 + ... + n. In S₆₄ − S₆₀, the terms 1 through 60 occur in both sums and cancel, leaving 61 + 62 + 63 + 64. Pairing the remaining terms gives (61 + 64) + (62 + 63) = 125 + 125 = 250. The standard formula confirms this: S₆₄ = 64×65/2 = 2080 and S₆₀ = 60×61/2 = 1830, so their difference is 2080 − 1830 = 250. Hence option C is correct. The other options can result from omitting a remaining term or making an arithmetic error.
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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