4G LTE on iPhone 5 On Verizon?

I got a iPhone 5 on Verizon and my city supports it but I'm not getting any LTE. Why
might this be? Any ideas

When there's no service area for your LTE around you it will revert to 3g, also depending on what kind of contract you have or plan you are using sometimes they give you 4g for a certain amount of time or data usage per month then it reverts to 3g in order to let you "test" out 4g so you can pay extra and buy it instead of 3g. There's probably a site that will show you verizon's 4g coverage per location, sometimes if the signal is weak it will just stick to 3g since it is easier and more common to find a signal for.