A reported drop in industrial production, preliminary signs is a rise in unemployment, and a cut in a major bank's prime lending rate combined yesterday to paint a picture of a slowly weakening economy.

The sharply higher oil prices, and now in prospect, possibly a large increase in gasoline taxes or some form of rationing, which President Carter said yesterday he is considering, could also hurt the economy in 1980, economists said.

Industrial production declind 0.5 percent in November, primarily because of a cutback in the output of autos, trucks, and related materials and parts, the Federal Reserve Board said.

Partly as a result of layoffs in the automobile industry and its suppliers, the number of persons receiving state unemployment benefits has begun to rise, the Labor Department said. While the figures are distorted by the Thanksgiving holiday, the number of claimants jumped by about 150,000 in the final weeks of November. If continued, the level of claims suggests the unemployment rate for December would rise to 6.0 percent or 6.1 percent from last month's 5.8 percent, economist Alan Greenspan estimated.

Meanwhile, Citibank, the nation's second largest, announced it was cutting its prime lending rate from 15 1/4 percent to 15 percent. A spokesman for the bank said the formula it uses for setting the prime -- which is keyed to certain short-term money market rate -- called for only a 14 3/4 percent rate, but that the bank had decided to change the rate only one-quarter of a point at a time.

The drop in the prime, which was not followed immediately by other major banks, was the result of shrinking demand for credit, especially by business, at large banks. The fall in credit demand, in turn, reflects the slowing of economic activity.

President Carter on Thursday told a group of editors of the Gannett newspaper chain he will decide soon on whether to ask Congress for higher gasoline taxes or additional rationing authority to cut gasoline consumption. A transcript of his remarks was released yesterday.

"Gasoline is obviously the easiest energy supply to curtail as far as waste is concerned, because Americans do waste so much," Carter said.

The president said voluntary actions might suffice. But he added. "An increase in the price of gasoline has shown, in the last few months, to be much closer related to conservation than we had previously anticipated . . . which has been a fairly pleasant surprise.

"We have experienced lately a 7 or 8 percent reduction in gasline consumption," Carter continued."I have not yet made a decision how to cut gasoline consumption more. We can do it without hurting our economy."

Even some of his own advisers do not necessarily agree with the latter assertion. A gasoline tax large enough to put a significant dent in use probably would have to be on the order of 50 cents a gallon, they believe, and that would add about five percentage ECONOMY, From E8 points to the level of consumer prices over a two-year period. Rationing, too, could put a crimp in many auto-related activities, including tourism.

In an interview yesterday, Rep. Al Ullman (D-Ore.), chairman of the House Ways and Means Committee, said he does not support the idea of a 50-cent gasoline tax, adding, "I don't think it's politically achievable."

"There would be very little support for it," Ullman said. "I supported a large tax in 1975, but there's a difference between a tax at 40 cents and a tax at $1 (a gallon pump price for gasoline)."

The Ways and Means chairman also reiterated his view that a tax cut to boost the economy would be "counter-productive."

"The economy as yet does not warrant a departure from sound fiscal policy," he said. "Inflation is such that it almost demands fiscal restraint." Whether other members of his tax-writing committee would seek a cut, he added, "depends on the nature of the economic problem. If the economy remains as it is today, the majority would be for fiscal restraint."

Separately from the gasoline tax question. Carter's advisers must make a recommendation shortly on whether the administration should propose any tax cut in connection with the 1981 budget, which goes to Congress next month.

The Federal Reserve said total industrial production in November was 151.6 percent of the 1967 average, less than 1 percent below its peak last March.