[tex]\displaystyle (x+1)+(x+2)+(x+3)+...+(x+100)=13450 \\ \\ 100x+(1+2+3+...+100)=100x+ \frac{100(100+1)}{2} = \\ \\ =100x+ \frac{100 \cdot 101}{2} =100x+50 \cdot 101=100x+5050\\ \\ 100x+5050=13450 \\ \\ 100x=13450-5050\\ \\ 100x=8400 \\ \\ x= \frac{8400}{100} \Rightarrow \boxed{x=84}[/tex]
