Cody is designing a pattern for a wood floor the length of the pieces of wood are 1 1/2 inches 1 13/16 inches and 2 1/8 inches what is the length of the fifth piece of wood if the pattern continues

Well, you only listed three pieces so far.  But I can already see a
pattern emerging from those three.

Of course, the next piece might return to 1-1/2 inches.  I mean,
the pattern can't just keep on going and increasing forever or
Cody would eventually wind up with pieces that are a mile long. 
It must eventually return to 1-1/2 inches and start over from there.

From the first piece to the second one, and from the second one
to the third one, the increase is  5/16 inch both times.  So if the
pattern is more than three pieces long before it starts over from
1-1/2, then the next piece is

             (2-1/8 + 5/16) = (2-2/16 + 5/16)  =  2-7/16 inches .