In a five-sided figure, the vertices are labeled $P,Q,R,S,$ and $T$. The numbers $2,4,6,8,$ and $10$ are assigned to these vertices, although not necessarily in this order. The sums of the numbers at the ends of the line segments $PQ,QR,RS,ST,$ and $TP$ form an arithmetic sequence, although not necessarily in this order. What is the middle term of the sequence?