Las Vegas’ apartment market has accelerated in recent years. Developers are packing the suburbs with projects, landlords are on a buying spree, and tenants are filling buildings. Rents are also rising at one of the fastest rates in the country, stretching affordability for some. The average asking rent for a Las Vegas apartment is $1,059, up more than 25 percent since early 2013, according to research firm Reis Inc. The rental market has gained speed amid strong job and population growth. And landlords, despite raising the rents, are having little trouble signing tenants.