What is the value of S₈₅ − S₈₀?
Answer and explanation
Correct answer: 415
By definition, S₈₅ = 1 + 2 + ... + 80 + 81 + 82 + 83 + 84 + 85, whereas S₈₀ = 1 + 2 + ... + 80. Subtracting cancels the common first 80 terms, leaving 81 + 82 + 83 + 84 + 85. Their sum is (81 + 85) × 5/2 = 166 × 2.5 = 415, or directly 81 + 82 + 83 + 84 + 85 = 415. Therefore option C is correct. The result is not the sum from 80 through 85 because the 80th term is already included in both partial sums and cancels. The other options reflect omission or incorrect inclusion of one of the remaining terms.
Frequently asked questions
What is the correct answer to this question?
415
Why is this the correct answer?
By definition, S₈₅ = 1 + 2 + ... + 80 + 81 + 82 + 83 + 84 + 85, whereas S₈₀ = 1 + 2 + ... + 80. Subtracting cancels the common first 80 terms, leaving 81 + 82 + 83 + 84 + 85. Their sum is (81 + 85) × 5/2 = 166 × 2.5 = 415, or directly 81 + 82 + 83 + 84 + 85 = 415. Therefore option C is correct. The result is not the sum from 80 through 85 because the 80th term is already included in both partial sums and cancels. The other options reflect omission or incorrect inclusion of one of the remaining terms.
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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