The sum of eight consecutive integers is 2004. What is the largest integer amoung them.
Let us say the lowest number is `T_1 = n` .
Then we can say;
`T_2 = n+1`
`T_3 = n+2`
`T_7 = n+6`
`T_8 = n+7`
So when we get the sum of them;
`n+(n+1)+(n+2)+(mn+3)+.......(n+7) = 2004`
`8n+1+2+....+6+7 = 2004`
`8n = 2004-7/2(7+1)`
`8n = 1976`
`n = 247`
So the largest number is `(n+7) = (247+7) = 254`
Largest number is 254.