Question

Insert four A.Ms between - 1 and 14.

Answer 1

-1 ,a1 ,a2,a3,a4,14  
let common difference of the A.P. is d then
14 = -1 + (6-1)d
15 = 5d
d = 3
hence four A.M. are 
a1 = -1+ 3 = 2
a2 = -1+6 = 5
a3 = -1+9 = 8
a4 = -1+12 = 11

Answer 2

am   =  a+b/2
       =(14-1)/2=13/2
similarly  (14-13/2)/2=15/2
again (15/2-13/2)/2=1/2
  (14-1/2)/2=27/2