The Treasury yesterday announced record borrowing needs of $41.25 billion for the first quarter of 1982 to finance the administration's projected deficit for this fiscal year of just under $100 billion. Three offerings are set for next week.

The previous record borrowing of $38.4 billion was set in the first quarter of last year. Second-quarter borrowings should be in the $10-$15 billion range, Treasury Undersecretary for Monetary Affairs Beryl Sprinkel told reporters. Analysts yesterday predicted the market would react negatively to the news of a record debt offering--about $3 billion more than expected--and expressed doubt that second-quarter borrowings could be held to the projected level.

Sprinkel also said Treasury has asked Congress to repeal the 4.5 percent interest rate ceiling on long-term Treasury bonds, which applies if more than $70 billion is sold. Currently, $67.5 billion of such bonds are outstanding, and Sprinkel said a long-term bond offering of $2.5 billion is set next week, which would hit the maximum.

He added that Secretary Donald Regan had sent Congress a bill on Tuesday to remove the interest-rate ceiling on savings bonds, currently 9 percent, and to peg the bonds to market rates. The new savings bonds would sell at 85 percent of the yield on five-year Treasury notes, if held for five years.

Sprinkel said the Treasury had not yet decided whether to stop selling securities to the public and turn the sale over to banks, brokers and savings institutions. He said he hoped a decision would be forthcoming in the next few months. The high volume of retail sales of securities has strained the Treasury's resources, and officials think offerings can be made more efficiently and cheaply by the private sector.

Three new offerings to raise $10 billion were announced yesterday--part of the $41.25 billion needed for the quarter. Of the $10 billion, $5.7 billion will be new cash and the rest will refinance debt. Next Tuesday, Treasury will auction $5 billion in three-year notes, with a minimum denomination of $5,000. On Wednesday, it will sell $2.5 billion in 10-year notes, with a minimum of $1,000. And on Thursday, it will try to raise the same amount through the sale of 29 3/4-year bonds, with a $1,000 minimum. Tenders for the three offerings are due by 1:30 p.m. on the day of the auction, at the Treasury here or Federal Reserve branches and banks, including Richmond and Baltimore.

Sprinkel said he thought the recession would reach bottom this spring. He expressed confidence the huge government borrowings could be made without upward pressure on interest rates caused by a "crowding out" of private-sector borrowing.

He explained that in a period of declining inflation, such as the country is experiencing now, investors begin selling the tangible assets they collected while inflation was rising and shifting their money into stocks and bonds. In such circumstances Sprinkel said he expects interest rates and inflation expectations to go down.

He pointed out that this cycle had occurred a number of times before, the most recent being in 1975-76. As the country came out of that recession it had very sizable budget deficits which he said were larger in relative size to the economy than they are likely to be this time.

After hitting its nadir in March 1975, the economy expanded for the rest of that year and through 1976. Interest rates were down during that period even though the deficit was very high but inflation expectations were ebbing.