Suppose that  a,b,c are in arithmetic progression then the line ax+by+c=0  passes through the fixed point l,m then l+m=

Given a,b,c  are in arithmetic progression, so that  b=a+c2Substitute b=a+c2  in the equation   ax+by+c=0ax+a+c2y+c=02ax+a+cy+2c=0a2x+y+cy+2=0  This represents the set of all lines passing through the point of intersection of 2x+y=0  and  y+2=0The point of intersection is  1,−2Hence l+m=1−2=−1