In a seven-sided polygon (heptagon), the vertices are labeled $V_1,V_2,V_3,V_4,V_5,V_6,$ and $V_7$. The numbers $1,2,3,4,5,6,$ and $7$ are assigned to these vertices, although not necessarily in this order. The sums of the numbers at the ends of the seven line segments forming the sides of the heptagon ($V_1{V}_2,V_2{V}_3,\dots ,V_7{V}_1$) form an arithmetic sequence, although not necessarily in this order. What is the middle term of the sequence?