LTE not working

I recently bought a used iPhone 5s to replace my iPhone 4 because I was not eligible for an upgrade. The guy at the store cut my old SIM card in order for it to fit into my used iPhone. However I only get 4g service and not LTE. I know that we get LTE service in this area because many of my friends have it. I also have a mobile share of 6gb so I should be able to get LTE