First & Merchants Corp., a Richmond bank holding company, announced a preliminary agreement yesterday to acquire Service National Bank of Crystal City in an exchange of cash totaling $3 million.

Services National, with one office and assets of more than $15 million, would be merged into First & Merchants National Bank, a statewide bank that is the Richmond firm's major subsidiary.

Owners of the five-year-old Services National, established with a goal of catering to special needs of military service personnel, would receive $24 in cash for each share of the Northern Virginia bank.

When Services National opened, it had sold 125,000 shares at $20 apiece. The bank's stock was traded earlier this year at under $17 a share but rose in recent weeks and closed at $21 bid in the over-the-counter market yesterday, after the proposed acquisition was announced. A week earlier, the stock was selling at $19 bid.

Services earned a record $186,976 ($1.50 a share) in 1978 compared with a loss of 17 cents a share the previous year. In the first quarter of 1979, the local bank's profits were $46,855 (37 cents), up 43 percent from $32,807 (26 cents) a year earlier.

Deposits on March 31 were $12.3 million compared with $9.8 million a year ago while loan volume rose to $8.9 million from $7.3 million.

Retired Army Gen. Frank Besson Jr., board chairman of Services National, said yesterday that a merger into First & Merchants "will allow us to serve our customers' banking needs and to compete more effectively with the numerous other banking institutions in the Arlington and Crystal City areas."

First & Merchants bank has 89 offices across the state and had assets of $1.9 billion on March 31. Deposits were $1.4 billion and loan volume was $1 billion as of the same date. The Richmond company is one of the the four largest bank firms in Virginia. CAPTION: Picture, FRANK BESSON JR. . . . "compete more effectively"