What is the sum of the natural numbers from 61 to 125?
Answer and explanation
Correct answer: 6045
To sum a consecutive range, subtract the sum through the number just before the starting value: 61 + ... + 125 = S_125 − S_60. Using S_m = m(m+1)/2, S_125 = 125 × 126/2 = 7875 and S_60 = 60 × 61/2 = 1830. Therefore the required sum is 7875 − 1830 = 6045. Equivalently, there are 125 − 61 + 1 = 65 terms with average (61 + 125)/2 = 93, giving 65 × 93 = 6045. Thus option B is correct; the alternatives usually result from omitting an endpoint or subtracting the wrong preceding sum.
Frequently asked questions
What is the correct answer to this question?
6045
Why is this the correct answer?
To sum a consecutive range, subtract the sum through the number just before the starting value: 61 + ... + 125 = S_125 − S_60. Using S_m = m(m+1)/2, S_125 = 125 × 126/2 = 7875 and S_60 = 60 × 61/2 = 1830. Therefore the required sum is 7875 − 1830 = 6045. Equivalently, there are 125 − 61 + 1 = 65 terms with average (61 + 125)/2 = 93, giving 65 × 93 = 6045. Thus option B is correct; the alternatives usually result from omitting an endpoint or subtracting the wrong preceding sum.
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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