I had a very similar question, and found the same answer that vivalamexico gave.
To get range, you need to keep your promotions focused on offense, not defense.
All 3 rough terrain bonuses, and all 3 smooth terrain bonuses.
It is *real* tempting in the heat of battle to choose Cover (to help them survive) or the instant heal (same). Those are useful, but they don't help get you to increased range.
Some folks here have talked about a gambit where you declare war on a nearby city-state with flat terrain. Bring in 2 or 3 archers (or comp bows), and station them 3 hexes from the CS.
- Move archer 1 forward one hex, and fire
- take the hit, move back, and heal
- Move archer 2 forward one hex (the same firing position), and fire
- take the hit, move back, and heal
- repeat as necessary to build up experience
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