SOLUTION: a. 1, 3, 5, 7, 9 b. 0, 50, 100, 150, 200 c. 3, 6, 12, 24, 48 d. 10, 100, 1,000, 10,000, 100,000 e. 9, 13, 17, 21, 25, 29 f. 1, 8, 27, 64, 125 Find the 100th term and the nt

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 
          
             
           
          
          
          
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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.
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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 
          
          
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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.
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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.
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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 

 


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Edwin