If [tex]x[/tex] is one of the component integers, then the next consecutive integer is [tex]x+1[/tex], the following one is [tex]x+2[/tex] and so on.
This means the sum can be written as
[tex]x+(x+1)+(x+2)+(x+3)=114[/tex]
Solving for [tex]x[/tex], you find that [tex]x=27[/tex], so the integers are [tex]27,28,29,30[/tex].
