Home sales dropped sharply in Northern Virginia last year, with 17 percent fewer transactions in 1982 when compared with 1981. The good news, however, is that the sagging sales all were recorded in the first eight months of the year, and sales increased from September through December.

In 1982, sales of 12,521 housing units were reported--a 17 percent drop from 1981, when 15,155 sales were recorded, according to the Northern Virginia Board of Realtors. The figures cover single-family home, condominium and townhouse sales.

But by December, the 1982 sales were a healthy 30 percent higher than in the same month in 1981, capping a four-month trend. A realtors' board spokesman attributed the improved sales to the drop in mortgage interest rates that began in August. Rates now stand at 12 percent for FHA and VA loans and around 2 percentage points higher on conventional mortgages.

Continuing inflation pushed up the cost of a new home in the Northern Virginia area in 1982, with the average price being $105,131. The 1981 average was $100,500.

The realtors' board based its reports on information gathered from its multiple listing service for Fairfax and Arlington counties, Alexandria and municipalities such as Falls Church, Vienna and Springfield.

The board's president, Richard Purvis, said while sales last year "started out slow and obviously suffering from high interest rates . . . the attitude of people on the street, the working agents and the buying public, is very positive" now. Purvis expects the recovery to be slow, but he is confident that it will come.