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Mrrafil [7]
3 years ago
10

If the sum of 4040 consecutive integer numbers is 2020, find out the absolute difference between the first number and the last n

umber.
Mathematics
1 answer:
bearhunter [10]3 years ago
4 0

Let x be the smallest of the consecutive integers summing to 2020. Then the largest integer in the sum is x+4039, so our answer is \boxed{4039}.

For completeness, though, let's solve for the value of x that satisfies the conditions of the problem. Recall that the sum of an arithmetic series with first term a_1, last term a_n, and n terms, is \frac{n(a_1+a_n)}{2}. Plugging in our known values gives us the equation \frac{4040(2x+4039)}{2}=2020, which simplifies to 2x+4039=1. Thus, x=-2019, so the 4040 consecutive integers are -2019,-2018,\dots,-1,0,1,\dots,2018,2019,2020. Notice how everything except the 2020 cancels out!

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