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14-01-2019
Mathematics

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the sum of 6 consecutive integers is 204. what is the fourth number in this sequence?

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LammettHash LammettHash

14-01-2019

Let [tex]x[/tex] by the smallest of the 6 integers. Then

[tex]x+(x+1)+(x+2)+(x+3)+(x+4)+(x+5)=204[/tex]

[tex]\implies6x+15=204[/tex]

[tex]\implies6x=189[/tex]

But 189 is odd, so it cannot be divisible by 6, which means [tex]x[/tex] is not an integer...

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