Equitable Bancorporation, the third-largest bank holding company in Maryland, announced first-quarter profits of $7.4 million (82 cents per share), up 49 percent from the $5 million (47 cents) for the same period of 1984.

The company also announced it had filed a registration statement with the Securities and Exchange Commission for an offering of 1 million shares of common stock.

* First American Bank NA of Washington experienced a 16 percent increase in profits for the first three months of 1985, as earnings rose to $1.8 million. Since all the shares of the bank are held by the parent corporation, First American Bankshares Inc., no per-share earnings figures are released.

* First American Bank of Maryland had a 25.5 percent rise in net income for the first quarter to $1.1 million ($1.08), compared with $853,000 (86 cents) for the same period of 1984. Net loans increased by 54 percent. The bank is partially owned by First American Bankshares.

* First-quarter profits at Baltimore Gas & Electric Co. dipped by 4.7 percent to $64.8 million ($1.47) from $67.99 million ($1.57) a year earlier. Revenue was $508 million compared with $522.7 million in the first quarter of 1984.

* Syscon Corp., a Washington developer of computer hardware/software products, reported earnings for the quarter ended Feb. 28 of $986,000 (32 cents), up 10 percent from $895,000 (29 cents) in the comparable 1984 period. Revenue amounted to $26.2 million, up 9 percent from $24 million.

* Atlantic Research Corp., a diversified technology company with headquarters in Alexandria, showed a profit of $3.7 million (88 cents) for the first quarter, compared with $2.15 million (51 cents) the previous year. Sale of its subsidiary Tri-Seal International accounted for $1.1 million (27 cents) of that profit. Revenue during the period totaled $45.7 million, up 22 percent over the first quarter of 1984.

* Dominion Resources Inc., a Richmond-based coal and nuclear power utility that is the holding company for Virginia Electric Power Co. (Vepco), saw net income rise 14.8 percent during the first quarter. Earnings rose to $89.5 million ($1.02), versus $77.96 million (94 cents) in 1984. Revenue for the period totaled $727 million.

* Avemco Corp., a Frederick, Md., aviation insurer, had profits of $1.59 million (52 cents) for the latest quarter, up slightly from $1.48 million (49 cents) a year earlier. Income from operations was $1.8 million, but a loss from investment sales of $204,000 reduced per-share earnings by 7 cents. Revenue for the quarter was $12.57 million, compared with $10.3 million for the year-earlier period.