a. 1, 3, 5, 7, 9

That's an arithmetic sequence with first term  and
common difference , because you always ADD 2 to get the next term.

So we use 
          
             
           
          
          
          
------------------------------------
b. 0, 50, 100, 150, 200

That's an arithmetic sequence with first term  and 
common difference , because you always ADD 50 to get the next term.

That one is done exactly like problem a.  I'll let you do that one
by yourself.
------------------------------------
c. 3, 6, 12, 24, 48

That's a geometric sequence with first term  and common
ration , because you always MULTIPLY BY 2 to get the next term.

So we use 
          
          
------------------------------------
d. 10, 100, 1,000, 10,000, 100,000

That's a geometric sequence with first term  and common 
ratio , because you always MULTIPLY BY 10 to get the next term.

That one is done exactly like problem c.  I'll let you do that one
by yourself.
------------------------------------
e. 9, 13, 17, 21, 25, 29

That's an arithmetic sequence with first term  and ,
because you always ADD 4 to get the next term.

That one is done exactly like problem a.  I'll let you do that one
by yourself.
------------------------------------
f. 1, 8, 27, 64, 125 

Now that one is different from the others because it is neither an 
arithmetic sequence nor a geometric sequence.  However we can recognize it
as the sequence of the cube of the successive positive integers.

1=1³, 8=2³, 27=3³, 64=4³, 125=5³

So 

 


------------------------------------

Edwin