we can write three consecutive integers like this:
[tex]n,n+1,n+2[/tex]we have that the sum of the 2nd and the 3rd integers is -17, then:
[tex](n+1)+(n+2)=-17[/tex]solving for n, we get the following:
[tex]\begin{gathered} (n+1)+(n+2)=-17 \\ \Rightarrow n+n+1+2=-17 \\ \Rightarrow2n+3=-17 \\ \Rightarrow2n=-17-3=-20 \\ \Rightarrow n=\frac{-20}{2}=-10 \\ n=-10 \end{gathered}[/tex]therefore, the three consecutive integers are -10, -9 and -8
