If the first term is a and the common difference is d,
then the first 5 terms are:

a, a+d, a+2d, a+3d, a+4d


The second term is 9, so we have the equation

a+d = 9

The fifth term is 21, so we also have the equation

a+4d = 21

So we have the system of equations:



Solve the first equation for a and substitute it in the
second equation:

       a = 9-d
(9-d)+4d = 21
  9-d+4d = 21
    9+3d = 21
      3d = 12
       d = 4

Then substitute d=4 in

       a = 9-d
       a = 9-4
       a = 5

So the sequence

a, a+d, a+2d, a+3d, a+4d

 is

5, 5+4, 5+2(4), 5+3(4), 5+4(4)

5, 9, 5+8, 5+12, 5+16

5, 9, 13, 17, 21

The first three terms are 5, 9, and 13.

Edwin