What are the nex three numbers in the following sequence? 4, 13/3, 14/3, 5, 16/3.

Ask yourself:  by what number (a fraction) must we multiply 4 to obtain 13/3?  Try (13)/(4*3).

Check:  Does     13
                          * 4 equal 13/3?  Yes.
                          4(3)

Check again.  Does    13            13
                                  *  =  14/3 ?  No
                                    4(3)          3

Try something different.  Convert 4 to 3(4)
                                                             
                                                               3

Then we have 12/3, 13/3, 14/3, 15/3, 16/3 (different numerators, same 
                                                                                       denominator)

Continuing, 17/3, 18/3, 19/3, and so on.

All about the same size in the city the game was