Citing prudent management, Suburban Bancorporation of Hyattsville reported yesterday that profits increased 13.3 percent in the third quarter and 7 percent in the first nine months of 1981 over the same period last year.

Suburban, a bank holding company for Suburban Trust Bank, the largest bank in the Maryland suburbs of D.C., earned $4.45 million (94 cents a share) from operations in the quarter, compared with $3.91 million (83 cents) in 1980.

For the first nine months, operating income was $13 million ($2.75) compared with $12.1 million ($2.57) last year, according to Robert F. Tardio, chairman and chief executive officer.

Loans at the end of September totaled $821 million, down $32 million from 1980. Deposits, however, have climbed $15 million to $1.26 billion.

First & Merchants Corp. of Richmond reported a 48.7 percent increase in third-quarter earnings, to a record $6.08 million ($1.77) from $3.9 million ($1.19) this time last year.

For the first nine months of 1981, F&M earnings rose to $14.3 million ($4.28) from $12.1 million ($3.71), a 15.4 percent year-to-year gain.

Chairman C. Coleman McGehee cited acquisition of the National Bank of Fairfax last summer as one of the reasons for the bank holding company's strong third quarter.

Reynolds Metals Co. of Richmond reported third-quarter net income of $1.50 a share, and Board Chairman David P. Reynolds said the company expects to report a loss in the fourth quarter.

Third-quarter net income for the second-largest U.S. aluminum producer totaled $29.5 million, down from $36.6 million ($1.88 per share) in the same quarter a year ago, Reynolds said.

"Weakness in the economy and lower margins had an impact on our performance," he said. "In view of these continuing trends, we anticipate a loss from operations in the fourth quarter."

Net sales for the third quarter this year totaled $906 million compared with $913.7 million for the same quarter in 1980.

For the first nine months of this year, Reynolds said, net income was $107.8 million ($5.52 per common) on sales of $2.7 billion.

The comparable figures for the first nine months of 1980 were $146.8 million net ($7.60) also on sales of $2.7 billion.