A Northern Virginia savings and loan association that tried but failed to lend its way aggressively out of the recession was merged into an out-of-state bank late Friday by government regulators.

The Federal Home Loan Bank Board approved the acquisition of Mount Vernon Savings and Loan of Arlington, and another S&L it owned in the Tidewater area, Middle Peninsula-Northern Neck Savings and Loan of Gloucester, by a new bank, First Florida Federal Savings Bank. It was created from First Florida Savings and Loan of Gainesville, and is itself a wholly owned subsidiary of Metropolitan Savings Bank in Brooklyn, N.Y.

The Federal Savings and Loan Insurance Corp., the government insurer of S&Ls, will pay First Florida an undisclosed amount to complete the transaction. Metropolitan will provide an $8 million cash infusion. It is expected the Virginia S&L will operate under the name Mount Vernon, a division of First Florida Federal Savings Bank.

In the last half of 1981, Mount Vernon was one of only three federally insured savings and loans in the metropolitan area operating in the black. Its new president, James F. Russell, pushed sales of high interest bearing jumbo certificates until 82 percent of the S&L's deposits were in such certificates. He also actively marketed variable rate mortgages and sold more than $100 million of its mortgages in the secondary market. Its assets jumped from $31 million at the end of 1980, when Russell took over, to $106 million a year later.

Mount Vernon was also one of the very few to make a profit in the first half of 1982, when it was making a monthly profit of $100,000. It was then that Mount Vernon acquired Middle Peninsula for $445,000 in cash, and Russell talked about the possibility of further mergers.

However, Mount Vernon suffered a loss of $600,000 during the second half of last year. Asset expansion stopped. Its ratio of net worth to insured deposits declined from 2.5 percent to an anemic 1.7 percent and government regulators were forced to act. Russell resigned in November. Mount Vernon's chairman and major stockholder cited "differences of style."