In the five-sided star shown, the letters A,B,C,D, and E are replaced by the numbers 3,5,6,7, and 9, although not necessarily in this order. The sums of the numbers at the ends of the line segments AB,BC,CD,DE, and EA form an arithmetic sequence, although not necessarily in this order. What is the middle term of the arithmetic sequence?[asy]
size(150);
defaultpen(linewidth(0.8));
string[] strng = {'A','D','B','E','C'};
pair A=dir(90),B=dir(306),C=dir(162),D=dir(18),E=dir(234);
draw(A--B--C--D--E--cycle);
for(int i=0;i<=4;i=i+1)
{
path circ=circle(dir(90-72*i),0.125);
unfill(circ);
draw(circ);
label(""+strng+"",dir(90-72*i));
}
[/asy]<spanclass=′latex−bold′>(A)</span>9<spanclass=′latex−bold′>(B)</span>10<spanclass=′latex−bold′>(C)</span>11<spanclass=′latex−bold′>(D)</span>12<spanclass=′latex−bold′>(E)</span>13