I've been thinking about putting a pergola in my back yard using 4x6 post mounted on top of a cement slab. I want it to be 8ftx16ft. I want to use 3 post in the rear of the pergola, and just 2 in the front. Do you think I can use 2x6x16 redwood for the span in front with just the 2 post? One on each side of the post? It will be all redwood. Thanks.
If it's an "open" roof system, then yes.
If it's a "closed" (solid) roof system, then it must be able to withstand snow loads. (I know, where you live you don't get snow, but to meet Code, it needs to support a minimum of 20 lbs. per square foot of snow.) Therefore, with a closed roof system 2 - 2x6 Redwood joists can span about 12' -6" when supporting 4' of roof.
How about moving the corner posts in 18" on each corner and provide a 18" overhang on each corner in the front.