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I don't know if this is fire or lethal damage, although I suspect it's fire.
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Blazing Arrow is lethal damage with a couple dot ticks of fire damage. The fire damage doesn't amount to much though.
Also, I'd add that because of the weapon redraw times being a problem that I wouldn't use archery in a "blapper" build. Switching back and forth from primary to secondary would only give you headaches over the time wasted drawing your weapon.
I love archery and it's a very fun set to play, it takes a bit of time to get used to its quirks but it's not as gimp as some would argue. I7 will only make it even better.