Sears, Roebuck & Co.'s net income for the year ended Dec. 31 rose 8.4 percent to a record $1.45 billion ($4.01 per share) despite a drop in fourth-quarter earnings, the company announced yesterday.

The previous record was $1.34 billion ($3.80).

Also, Gannett Co. Inc. posted a 23 percent rise in fourth-quarter profits despite continuing heavy investments in operating costs for USA Today, while Armco Inc. said its fourth-quarter loss widened to $64.5 million from $46.8 million a year earlier, and blamed the losses on a surge in imported steel.

Sears said 1984 revenue totaled a record $38.83 billion, an increase of $2.95 billion, or 8.2 percent, from the previous record of $35.88 billion in 1983.

"One of the most competitive Christmas shopping seasons in history and unseasonably warm temperatures" had an adverse effect on the company's fourth quarter, said Sears Chairman and Chief Executive Officer Edward Telling.

But Telling remained positive about the overall showing in 1985.

Sears' fourth-quarter consolidated net income was $563.1 million ($1.54), compared with the record of $582.7 million ($1.65) in 1983. Fourth-quarter revenue rose 5.1 percent to $11.37 billion from $10.82 billion a year ago.

Telling said Sears' merchandise, insurance and real estate groups established records in net income and revenue for the full year.

* Gannett Co. Inc.'s earnings for 1984 rose 17 percent above 1983 levels.

Gannett publishes 85 daily newspapers and 35 non-dailies, and operates six television stations, 16 radio stations and the largest outdoor advertising company in North America.

Fourth-quarter net income climbed to $74.5 million (93 cents a share) from $60.8 million (76 cents) in the year-previous period. Operating revenue for the quarter was $570.1 million, up from $477.1 million.

For 1984, net income was $223.9 million ($2.80), up from $191.7 million ($2.40) in 1983. Operating revenue in 1984 advanced 15 percent to $1.96 billion from $1.7 billion.

USA Today's fourth-quarter advertising volume increased 78 percent over the prior year, and operating losses for the quarter were lower than in the comparable 1983 period, the company said.

Fourth-quarter newspaper advertising linage rose 13 percent, broadcast revenue increased 22 percent, and Gannett's outdoor advertising operation saw an 11 percent gain in revenue.

Last week, Gannett announced a tentative agreement to purchase the Des Mones Register and the Jackson Sun. The closing is expected in June.

* Armco Inc., a diversified metals manufacturer based in Middletown, Ohio, said that, despite the dismal fourth quarter, its loss for the full year narrowed to $295 million from $672.5 million lost a year earlier.

The company has sold some financial services subsidiaries, is trying to market others and has sold its West Virginia coal operations in the past year.

The fourth-quarter loss came on sales of $1.12 billion, up from $1.07 billion a year earlier. For the full year, the company's sales rose to $4.54 billion from $4.16 billion in 1983.

Counting only continuing operations, the company reported a loss of $64.8 million in the fourth quarter, compared with a profit of $40.4 million in the last three months of 1983. For the year, the company had a loss from continuing operations of $135.6 million, compared with a loss from continuing operations of $496.7 million a year ago.