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Pure bash 166

printf -v l %$[$1/2]s
echo "  ${l// /____}"
(($1%2))&&r=''||r=' /'
printf -v l %$[(1+$1)/2]s
echo "${l// / /\\ }$r"
printf -v l %$[(1+$1)/2]s
echo ${l// //__\\}${r# }

In action:

triangle() {
    printf -v l %$[$1/2]s
    echo "  ${l// /____}"
    (($1%2))&&r=''||r=' /'
    printf -v l %$[(1+$1)/2]s
    echo "${l// / /\\ }$r"
    printf -v l %$[(1+$1)/2]s
    echo ${l// //__\\}${r# }
}

then now:

for i in {1..12};do echo $i ;triangle $i;done
1
  
 /\ 
/__\
2
  ____
 /\  /
/__\/
3
  ____
 /\  /\ 
/__\/__\
4
  ________
 /\  /\  /
/__\/__\/
5
  ________
 /\  /\  /\ 
/__\/__\/__\
6
  ____________
 /\  /\  /\  /
/__\/__\/__\/
7
  ____________
 /\  /\  /\  /\ 
/__\/__\/__\/__\
8
  ________________
 /\  /\  /\  /\  /
/__\/__\/__\/__\/
9
  ________________
 /\  /\  /\  /\  /\ 
/__\/__\/__\/__\/__\
10
  ____________________
 /\  /\  /\  /\  /\  /
/__\/__\/__\/__\/__\/
11
  ____________________
 /\  /\  /\  /\  /\  /\ 
/__\/__\/__\/__\/__\/__\
12
  ________________________
 /\  /\  /\  /\  /\  /\  /
/__\/__\/__\/__\/__\/__\/