How much greater is the sum of the first (120) natural numbers than the sum of the first (60) natural numbers?
Answer and explanation
Correct answer: (5430)
The sum of the first n natural numbers is \\(S_n=\frac{n(n+1)}{2}\\). The question asks for how much larger the first 120-number sum is than the first 60-number sum, so we must subtract the smaller sum from the larger one. This avoids confusing the requested difference with either individual total.
For 120 numbers, \\(S_{120}=\frac{120\times121}{2}=7260\\). For 60 numbers, \\(S_{60}=\frac{60\times61}{2}=1830\\). Hence the required difference is \\(7260-1830=5430\\). Equivalently, it is the sum of the numbers from 61 through 120. Thus option C, 5430, is correct; values such as 5380 or 5480 result from an arithmetic error.
Frequently asked questions
What is the correct answer to this question?
(5430)
Why is this the correct answer?
The sum of the first n natural numbers is \\(S_n=\frac{n(n+1)}{2}\\). The question asks for how much larger the first 120-number sum is than the first 60-number sum, so we must subtract the smaller sum from the larger one. This avoids confusing the requested difference with either individual total.
For 120 numbers, \\(S_{120}=\frac{120\times121}{2}=7260\\). For 60 numbers, \\(S_{60}=\frac{60\times61}{2}=1830\\). Hence the required difference is \\(7260-1830=5430\\). Equivalently, it is the sum of the numbers from 61 through 120. Thus option C, 5430, is correct; values such as 5380 or 5480 result from an 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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