What is the value of S_250 − S_240?
Answer and explanation
Correct answer: 2455
The notation S_m denotes the sum of the first m natural numbers. When S_240 is subtracted from S_250, the terms from 1 through 240 cancel, leaving 241 + 242 + ... + 250. There are 10 terms in this arithmetic sequence. Its average is (241 + 250)/2 = 245.5, so its sum is 10 × 245.5 = 2455. Equivalently, S_250 − S_240 = [250 × 251 − 240 × 241]/2 = (62750 − 57840)/2 = 4910/2 = 2455. Hence option A is correct; the nearby alternatives reflect small addition or endpoint-counting errors.
Frequently asked questions
What is the correct answer to this question?
2455
Why is this the correct answer?
The notation S_m denotes the sum of the first m natural numbers. When S_240 is subtracted from S_250, the terms from 1 through 240 cancel, leaving 241 + 242 + ... + 250. There are 10 terms in this arithmetic sequence. Its average is (241 + 250)/2 = 245.5, so its sum is 10 × 245.5 = 2455. Equivalently, S_250 − S_240 = [250 × 251 − 240 × 241]/2 = (62750 − 57840)/2 = 4910/2 = 2455. Hence option A is correct; the nearby alternatives reflect small addition or endpoint-counting errors.
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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