The Washington Post has signed an agreement with Videotex America, a new California-based media company, to explore the videotex market in the Washington area.

Videotex is the generic name for an electronic service that allows consumers with the appropriate computer terminal to receive information and games, send electronic mail and do home banking transactions.

Some experts believe that videotex service will be a multibillion-dollar business by the end of the decade, although it's commercial acceptance has yet to be determined. The service is comparable to the use of home computers as information network terminals.

Videotex America, a joint venture of the Times Mirror Co. and Infomart, a Canadian company, has said it will launch Gateway, its videotex service, in Southern California by spring of next year. Gateway was tested in 350 households in 1982 and yesterday's agreement will give the Post access to the results of that test and the commercial operation.

"The Post wants to learn all it can about videotex in its infancy," said Post publisher Donald E. Graham. "We believe there may be substantial demands for the service in the future and we want to be ready to provide it."

Knight-Ridder Newspapers Inc. and American Telephone and Telegraph Co. are currently testing a videotex system in Coral Gables, Fla. It is scheduled for commercial service this September. AT&T also has a videotex experiment under way with CBS Inc. in Ridgefield, N.J. and says it intends to play a major role in the videotex market.