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

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christiano-cr7 | (Level 1) Salutatorian

Posted July 7, 2013 at 6:06 AM via web

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

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jeew-m | College Teacher | (Level 1) Educator Emeritus

Posted July 7, 2013 at 6:13 AM (Answer #1)

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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.

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