What is the value of S_250 − S_240?
Answer and explanation
Correct answer: 2455
The governing concept is the sum of the first n natural numbers, S_n = n(n+1)/2. In the difference S_250 − S_240, the terms 1 through 240 occur in both sums and cancel. The terms left are 241, 242, ..., 250, which contain 10 numbers. Their average is (241 + 250)/2 = 245.5, so their sum is 10 × 245.5 = 2455. The formula gives the same check: [250 × 251 − 240 × 241]/2 = [62750 − 57840]/2 = 2455. Therefore option A is correct. Options B, C, and D can result from a small subtraction error or incorrect endpoint counting.
Frequently asked questions
What is the correct answer to this question?
2455
Why is this the correct answer?
The governing concept is the sum of the first n natural numbers, S_n = n(n+1)/2. In the difference S_250 − S_240, the terms 1 through 240 occur in both sums and cancel. The terms left are 241, 242, ..., 250, which contain 10 numbers. Their average is (241 + 250)/2 = 245.5, so their sum is 10 × 245.5 = 2455. The formula gives the same check: [250 × 251 − 240 × 241]/2 = [62750 − 57840]/2 = 2455. Therefore option A is correct. Options B, C, and D can result from a small subtraction error or incorrect endpoint counting.
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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