A cable television system in Arlington County, originally set to begin operations in 1975, is expected to begin transmissions to subscribers in mid-June, spokesmen for the system said last week.

Thomas W. Richards, president of Arlington TeleCommunications Corp., which owns the cable system, said that financing has been arranged for the 360-mile, 36-channel system and construction will begin in May.

The system initially will offer 30 channels to Arlington viewers, said Richard S. Howe, marketing director for the firm. The channels will include all Washington and Baltimore commercial stations, four educational stations the Christian Broadcasting Network and automated information channels featuring news wire reports and weather forecasts.

Howe said the service will be available to 72,000 Arlington homes for $7.95 a month. Customers will have the option of receiving an extra channel featuring uninterrupted premiere movies, sports shows, specials and children's films for an additional $8.95 a month. Initially, he said, the sports programs will not include live coverage. Service for additional sets in a house will cost $2 a month, Howe added, and the installation charge for the cable service will be $25.

Howe explained that one channel in the cable system will be for Atlanta station WTCG, an independent station not affiliated with a major network. Arlington TeleCommunications hopes to quickly add KTVU, a San Francisco area station, and WGN, a Chicago station, both independents.

The independent stations will offer shows not produced by the three major television networks as well as network programs and movies in different time slots than regularly scheduled in Washington, Howe said.

Beginning in June, the service will be available to residents in the Clarendon area of Arlington and will be extended in the county at a rate of about 20 miles a month, said John Evans, vice president of Arlington Telecommunications. The company plans to make the system available to the entire county within 20 months of the initial hook-up, he said.

The system was financed by a $2 million equity investment by Business Development Services, Inc., a subsidiary of General Electric Co., with the remaining $4.7 million coming from a loan from the American Security Bank of Washington.

Tony Gardner, chief of fiscal analysis for Arlington County, said the county will receive 4 percent of gross receipts from the system, or a minimum of $12,000, through the business privilege tax.

Howe said one channel in the system will be reserved for public access, two for use by the county government and four for the school system.

Arlington TeleCommunications announced this week that Scientific Atlanta Inc. of Atlanta, Ga. had agreed to a $2.5 million project to provide the system with a signal processor, signal generation equipment and technical services. The signal processor, which will be located on top of Tower Villas at 3800 No. Fairfax Ave., Arlington, will collect broadcast signals in the area and send them over the cable system. The signal generation equipment will include an earth station at the Arlington TeleCommunications center at 2701 Wilson Blvd. The earth station will receive broadcast transmissions from stations relaying their signals by satellite.