What is the value of S_300−S_285, where S_n is the sum of the first n natural numbers?
Answer and explanation
Correct answer: 4395
Since S_n=1+2+...+n, subtracting S_285 from S_300 cancels all terms from 1 through 285. The governing idea is that only the remaining terms 286 through 300 must be added. There are 15 terms, their first and last terms are 286 and 300, and their average is (286+300)/2=293. Therefore the difference is 15×293=4395. Equivalently, S_300−S_285=300×301/2−285×286/2=45150−40755=4395. Thus option B is correct; the other values reflect an incorrect term count or arithmetic error.
Frequently asked questions
What is the correct answer to this question?
4395
Why is this the correct answer?
Since S_n=1+2+...+n, subtracting S_285 from S_300 cancels all terms from 1 through 285. The governing idea is that only the remaining terms 286 through 300 must be added. There are 15 terms, their first and last terms are 286 and 300, and their average is (286+300)/2=293. Therefore the difference is 15×293=4395. Equivalently, S_300−S_285=300×301/2−285×286/2=45150−40755=4395. Thus option B is correct; the other values reflect an incorrect term count or 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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