The nation's federally insured savings and loan associations lost a record $3.1 billion in the last half of 1981, double the loss posted in the first half of the year, the government reported yesterday.

The Federal Home Loan Bank Board also said that nearly 85 percent of the 3,786 government-insured S&Ls showed losses in the last half compared with 70 percent in the first half.

The FHLBB blamed the huge losses on the widening gap between what thrifts must pay to obtain new funds and what they earn on holdings of past mortgage loans. It said savings and loans paid an average of 11.53 percent in interest costs to obtain operating funds in the second half, up from 10.31 percent in the first half, but earned an average rate of 10 percent on their mortage loan holdings in the second half, up slightly from 9.72 percent in the first half. add F

ARCO PRICE CUT: Atlantic Richfield Co., the eighth-largest U.S. gasoline marketer, has cut its wholesale gasoline prices 2.8 cents a gallon to reflect the company's elimination of credit cards on April 15.

Arco also said it has dropped its dealer rebate program and reduced gasoline prices an additional 4 cents a gallon in a move that affects only about 25 percent of its dealers.