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}#

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

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

Solving for #x#:

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

#=> 3x+3 = 2x+7#

#=> 3x-2x = 7-3#

#:. x = 4#

Checking our result:

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

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