What factors drew an increasing number of Americans into the West? How did the settlement and development of these lands affect American Indians' lives?

Many factors drew people west. Manifest Destiny, the idea that it was our "God-given right" to control all the land "from sea to shining sea" was one. The vast amount of land that was being sold extremely cheaply of given away for free meant people could more easily establish farms with little to fear of the initial debt. Add in the finding of gold and other precious metals, meant that some people were pulled west by the idea that they could get rich without having to work very hard.

As for Native Americans, they were increasing pushed out of their native lands. If they refused to move then things often turned violent which meant almost extinction for their people.