The sum of 2023 consecutive integers is 2023. What is the sum of digits of the largest of these integers? A 4 B 5 C 6 D 7 8 E
Question
The sum of 2023 consecutive integers is 2023. What is the sum of digits of the largest of these integers? A 4 B 5 C 6 D 7 8 E
Solution
The sum of n consecutive integers starting from x is given by the formula n/2 * (2x + n - 1).
Given that the sum is 2023 and there are 2023 integers, we can set up the equation 2023 = 2023/2 * (2x + 2023 - 1).
Solving for x gives us x = -1010.5.
However, x must be an integer, so we round up to -1010.
The largest integer in the sequence is therefore -1010 + 2023 - 1 = 1012.
The sum of the digits of 1012 is 1 + 0 + 1 + 2 = 4.
So, the answer is A. 4.
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