What is the sum of the natural numbers from 91 to 100?
Answer and explanation
Correct answer: 955
The relevant concept is a partial sum of consecutive natural numbers. Use the first-n sum formula Sₙ = n(n + 1)/2. The sum from 91 through 100 equals the sum through 100 minus the sum through 90: S₁₀₀ − S₉₀ = [100 × 101/2] − [90 × 91/2] = 5050 − 4095 = 955. Therefore option C is correct. A second check uses the arithmetic-series idea: there are 10 terms, their average is (91 + 100)/2 = 95.5, and 10 × 95.5 = 955. Options A, B, and D are close distractors caused by endpoint, counting, or subtraction mistakes; the endpoints 91 and 100 must both be included.
Frequently asked questions
What is the correct answer to this question?
955
Why is this the correct answer?
The relevant concept is a partial sum of consecutive natural numbers. Use the first-n sum formula Sₙ = n(n + 1)/2. The sum from 91 through 100 equals the sum through 100 minus the sum through 90: S₁₀₀ − S₉₀ = [100 × 101/2] − [90 × 91/2] = 5050 − 4095 = 955. Therefore option C is correct. A second check uses the arithmetic-series idea: there are 10 terms, their average is (91 + 100)/2 = 95.5, and 10 × 95.5 = 955. Options A, B, and D are close distractors caused by endpoint, counting, or subtraction mistakes; the endpoints 91 and 100 must both be included.
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.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
