Armco Inc., a diversified metals and resources concern, said yesterday its first-quarter profits fell 75 percent from a year earlier, mainly because of the recession.

Armco, 51st largest U.S. firm in sales, according to the 1981 Fortune 500 list, said profits fell to $17.7 million (26 cents a share) from $69.7 million ($1.21) a year earlier. Sales edged up to $1.65 billion from $1.63 billion.

Besides the recession, Armco attributed its results to high interest rates, the oil glut and a substantial increase in imports of steel products, including carbon steels, stainless steels and oil-country tubular goods.

BankAmerica Corp. reported yesterday that earnings before securities transactions rose 3.4 percent from the year-ago period, while Chase Manhattan Corp. reported a jump of 58 percent in the first three months of 1982.

BankAmerica, San Francisco-based holding company for the nation's largest bank, earned $115.7 million (78 cents) before securities transactions, compared with earnings of $111.8 million (76 cents) a year ago.

New York-based Chase, whose subsidiary bank is the industry's third largest, had operating earnings of $116.2 million ($3.24), up from $73.5 million ($2) in the first quarter of 1981.

Chase attributed its earnings gain principally to a 35 percent increase in net interest income to $565 million. BankAmerica said the latest gain was due "significantly" to improved international results.

United Technologies, a designer and builder of high-technology products, said yesterday that first-quarter profits were down 16 percent from a year earlier.

The firm, ranked 20th in the Fortune 500, reported first-quarter net income of $162.14 million ($2.46, fully diluted), which included the cumulative effect of an accounting change for investment tax credits of $66.62 million. In the comparable quarter in 1981, net income was $113.58 million ($1.84).

Sales for the quarter totaled $3.214 billion, a 4 percent decline from $3.345 billion in the first quarter of 1981.

Great Western Financial Corp., parent of the nation's second-largest savings and loan association, said yesterday it lost $14.6 million in the first quarter, a sharp reversal from its 1981 first-quarter profit of $841,000 (4 cents a share).

First-quarter revenue for the parent company of Great Western Savings & Loan was $293.9 million compared with $274.5 million a year ago.

Great Western, with 123 offices and total assets of $10.5 billion, is the largest S&L behind Home Savings, a unit of H.F. Ahmanson & Co.

Great Western Chairman James Montgomery blamed the loss on stubbornly high interest rates, but noted the operating losses for the first quarter were less than those for the fourth quarter of 1981.

American Express Co. reported first-quarter profit rose 7.9 percent from a year earlier, mainly on improved earnings by its travel-related operations such as the American Express charge card.

The company, the nation's fourth-largest diversified financial company, said net income rose to $117.6 million ($1.25) from $109.0 million ($1.19) in the same quarter last year. Revenue increased 8 1/2 percent to $1.79 billion from $1.65 billion.