Display a chain of little mountains with an odd number on the top of it!

05AB1E, 19 15 14 12 bytes

05AB1E uses CP-1252 encoding.
Saved 4 bytes thanks to Adnan.
Saved 2 bytes thanks to carusocomputing

ÅÉðìDg…/ \×»

Try it online!

Explanation

ÅÉ               # list of uneven number up to input
  ðì             # prepend a space to each
    Dg           # get length of list
      …/ \       # push the string "/ \"
          ×      # repeat the string length-list times
           »     # join rows by spaces and columns by newlines

Pyke, 16 bytes

S2%idm+dJil*"/ \

Try it here!

17 bytes and more awesome

S2%i`~Bd.:il*"/ \

Try it here!

This uses IMHO an AWESOME algorithm for making sure the first line is correctly aligned.

S                 - range(1, input+1)
 2%               -  ^[::2]
   i              -   i = ^
    `             -    str(^)
     ~Bd.:        -     ^.translate("><+-.,[]", " ") <-- awesome bit here
          il      -  len(i)
            *"/ \ - ^ * "/ \"

This replaces all the characters in the stringified list with spaces. ~B contains all the characters in the Brain**** language and this is the first time I've used this variable.

The program `~Bd.: does this:

`~Bd.: - input = [1, 3, 5, 7]
`      - str(input)  # stack now ["[1, 3, 5, 7]"]
 ~B    - "><+-.,[]"  # stack now ["[1, 3, 5, 7]", "><+-.,[]"]
   d   - " "         # stack now ["[1, 3, 5, 7]", "><+-.,[]", " "]
    .: - translate() # stack now [" 1  3  5  7 "]

Python 2 3, 67 65 63 60 Bytes

Nothing too crazy here, I think the first section can probably be done shorter but I'm not quite sure how. I use the fact that in this case -~n/2 will work for ceil.

lambda n:-~n//2*' %d '%(*range(1,n+1,2),)+'\n'+-~n//2*'/ \\'

Below are alternative 61 and 65 byte solutions in Python 2:

lambda n:-~n/2*' %d '%tuple(range(1,n+1,2))+'\n'+-~n/2*'/ \\'
lambda n:' '+'  '.join(map(str,range(1,n+1,2)))+'\n'+-~n/2*'/ \\'

^{Thanks to Rod for saving 2 bytes and Artyer for saving another byte by switching version :)}