How do you find a set of three consecutive integers whose sum is equal to the sum of the next two consecutive integers immediately following them?

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Answer 1 · 2016-05-20T19:39:57

${4, 5, 6}$ ${4, 5, 6}$

Let $x$ $x$ be the least of the first three integers. Then the set consists of ${x, x + 1, x + 2}$ ${x, x+1, x+2}$ where

$x + (x + 1) + (x + 2) = (x + 3) + (x + 4)$ $x+(x+1)+(x+2) = (x+3)+(x+4)$

Solving for $x$ $x$ :

$x + (x + 1) + (x + 2) = (x + 3) + (x + 4)$ $x+(x+1)+(x+2) = (x+3)+(x+4)$

$\Rightarrow 3 x + 3 = 2 x + 7$ $=> 3x+3 = 2x+7$

$\Rightarrow 3 x - 2 x = 7 - 3$ $=> 3x-2x = 7-3$

$:. x = 4$

Checking our result:

$4 + 5 + 6 = 15 = 7 + 8$

Thus, we have our answer as ${4, 5, 6}$