高一英语选择题.They elected him___captain of the team for ___second

高一英语选择题.They elected him___captain of the team for ___second time.
They elected him___captain of the team for ___second time.
答案是/,a. 为什么第二格不是the?我觉得也通的呀.
求解答

1.第一空：职位、官衔前不加the；
2.第二空：a 才对!
因为“a second time”“又一次,再一次”之义.
“the second time”（表顺序）“第二次”
全句：他们第二次选举他当队长.