Each repeater cuts in 1/2. So after the 3rd or 4th repeater....wow, you'd be a dial up speeds.
The way to do larger networks that require multiple access points...is to use access points that are designed to be centrally managed ...these are business grade access points. Don't go trying to make a bubblegum and duct tape wireless setup out of a bunch of home grade units. Leave repeaters for little home networks.
Some of my preferred hardware for larger wireless deployments....HP ProCurve MSP units. It's pricey..yes...you'll be started with at least 4 grand in hardware just to get 3-4 access points out...but it's economical if you have a network large enough to use at least a dozen or more. Rock solid units.
If you're on a smaller budget, take a look at Ubiquity Unifi products...
I've done some networks with those...you install the management software on a server or PC ..and control them from there. Less than a hundred bucks per AP....and they work quite well.