# Python 3, <s>90</s> 80 bytes



<!-- language: lang-py -->

    def F(s,n,i=2,O='-/+*'):
     while i<n:s+=[eval(str(s[-2])+O[i%4]+str(s[-1]))];i+=1

This function modifies the list passed to it. Use like this:

    s = [1,3] 
    F(s,8)