Virginia's unemployment rate rose to 7.8 percent in October, substantially higher than the 5.6 percent jobless rate of a year ago and slightly higher than it was in September.

Of the state's urban areas, only Northern Virginia, where federal employment still provides a measure of stability, escaped an increase in the jobless rate from the month before.

The Virginia Employment Commission said that an increase in the work force coupled with slack seasonal employment in agriculture had combined to boost the number of out-of-work Virginians to 205,800. Officials predicted that the situation could get even worse during the holiday season as teen-agers and housewives look for jobs for extra income and cold weather curtails out-of-doors work.

Officials pointed out that Virginia's unemployment rate remains below national levels. "As usual, a large number of governmental employes and broad industrial diversification left Virginia in a good posture compared to many areas of the nation," said William F. Mezger of the VEC.

In October unemployment normally declines in Virginia because of the number of people going back to school and an increase in harvest activity. But this year unemployment rose to 7.8 percent from 7.4 percent in September. The labor force grew by approximately 2,000, and state officials said they could not explain why. At the same time, fewer agricultural workers were needed than usual for this time of year because of frost damage to fruit and an early end of the tobacco harvest .

Unemployment in the Roanoke area was 7.9 percent, pushed up by factory and railroad layoffs. The jobless rate for the Norfolk-Virginia Beach-Portsmouth area was 7.7 percent. In Newport News-Hampton it was 7 percent, and in Richmond it was 5.9 percent. Northern Virginia's unemployment rate remained unchanged at 4.3 percent.

The worst hit area of the state was southwest Virginia where the recession in coal mining has taken a heavy toll. Dickenson County had the highest unemployment rate at 24.8 percent. Buchanan County had a jobless rate of 22.1 percent. Russell County's unemployment was 21.9 percent, and Tazewell County's jobless rate was 19.4 percent.