# The sum of eight consecutive integers is 2004. What is the largest integer amoung them.

### 1 Answer | Add Yours

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.*