Financial General Bankshares Inc., the giant 12-bank holding company, yesterday announced a drop in third-quarter profits and attributed it to the cost of installing a large automated-teller system and the failure of interest income to keep pace with rising costs.

For the quarter, Financial General reported profits dropped 7.6 percent to $3.94 million (54 cents a share) from 1979 third-quarter profits of $4.26 million (58 cents).

The bank also reported a 2 percent rise in nine-month profits to $11.72 million ($1.61) from $11.49 million ($1.57) for the same period last year.

In other reports, Dynalectron Corp. reported a rise in Third-quarter and nine-month earnings. The McLean company said profits for the quarter were $610,000 (8 cents a share), up from 1979 third-quarter profits of $554,000 (8 cents).

Nine-month profits were $2.41 million (33 cents) compared with $1.54 million (22 cents) for the same period last year.

Revenues for the quarter rose to $114.3 million from $88 million last year, and those for the nine-month period rose to $317.5 million from $250.1 million.

The Ryland Group Inc. has reported a 36 percent drop in third-quarter profits to $1.61 million (52 cents a share) from $2.51 million (78 cents) for the same quarter last year.

For the first nine months of the year, the housing construction company reported profits of $4.41 million ($1.42), down from $5.30 million ($1.64).