Question 20. The sum of 2023 consecutive integers is 2023. What is the sum of digits of the largest of these integers? To start this problem, we need to recognize that we will be using negative numbers. Otherwise it will be impossible to get a sum of 2023 starting at 1 or 0. And then going up consecutively. So we start off with an example of negative 1, 0, and 1. With these three consecutive integers, we get a sum of 0. Now if we had a 2 at the end and had four consecutive integers, we would have a sum of 2. So we just need to take 2023 divided by 2 and get a total of 1011 and a half. This has to be full regular integers. So if we take a look at something like this, which gives us 2023 consecutive integers, with a 0 being the number in the middle, our sum would be 0. If we shifted this over by 1, starting off at negative 1,010 and ending at 1,012, every number would cancel itself out. Negative 1,010 would sum with 1,010 and make 0. Negative 1,009 with a 1,009 all together would go down to 0, leaving us just with 1,011 plus 1,012, giving us 2023. Now the sum of the digits of the largest of these integers will be 1 plus 0 plus 1 plus 2. So our answer will be A, 4.

consecutive integers

sum

largest integer

sum of digits

mathematics problem