3. The sum of 2024 consecutive even integers is 1,171,896. What is the largest of these numbers?
First solution.

Since we are dealing with consecutive even numbers (the difference between adjacent numbers is constant), the arithmetic mean of all numbers is equal to the arithmetic mean of the first and last number.

Let $n$ be the desired number.

Then $n-4046$ is the first of 2024 consecutive even integers.

2 POINTS

We have:

$\frac{(n-4046)+n}{2}=579$

$n-2023=579 \quad 2$ POINTS

$n=579+2023=2602 \quad 1$ POINT

TOTAL 10 POINTS

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