The output of the nation's factories, minies an dutilities continued to increase at a moderately brisk pace in September, helping allay fears that an economic slowdown is in the near future.

The Federal Reserve Board said that industrial production grew 0.5 percent in September, as fast as in August, and at a rate consistent with administration forecasts that the overall economy will grow at an annual rate of about 3.5 percent in the final three months of 1978.

While that rate of economic growth is not enough to make serious dents in the unemployment rate - which was 6 in percent in September, about where it's been for the last eight months - it is belived to be sufficiently lare to keep the rate from rising.

The Federal Reserve said that the growth of output probably would have been slightly higher if there had not been a railroad strike in the last few days of September.

Theodore Torda, a senior Commerce Department economist, called the 0.5 percent rise in industrial production a "reasonably good figure . . . It does tell us there's a good bit of strength" left out there in the economy.

Many administration analysis and private economists are becoming worried that the sharp increase in interest rates that has occurred since last April as well as the continuing high level of inflation could bring the three-and-a-half year economic expansion to an end.

Interest rates have been rising in part because the Federal Reserve is trying to raise them to fight inflation and in part because of demand for credit from businesses and consumers remains strong.

The prime rate now stands at 10 percent and the Federal Reserve Board last Friday boosted its discount rate - the interest it charges member banks who borrow from it - to 8.5 percent, a record.

Many analyais think the half-point boost in the discount rate sets the stage for further open market tightening actions by the central bank. The Federal Open Market Committee, which sets monetary policy, met at the Federal Reserve yesterday.

Monday market observers will watch the Fed's trading desk today to see if they can perceive a further tightening in monetary policy. The Fed tightens monetary policy by selling government securities, sopping up funds banks otherwise might lend. It keys its policies to the federal funds rate (the interest banks charge each other for overnight loans of excess reserves).

The Fed's target rate for federal funds is now about 7/8 percent. Experts think that rate could pass 9 percent shortly.

The Fed said that the 0.5 percent rise in industrial production "reflected further advances in the production of equipment, business and construction supplies, and materials."

The industrial production index was at 147.5 percent, 6.5 percent above a year ago. The index rose at a 7.7 percent annual rate in the third quarter.

In part because of the rail strike, automobile production fell from an annual rate of 9.4 million units to 8.9 million units.

As a result, production of consumer durable goods fell 0.7 percent last month. Overall consumer goods production rose 0.1 percent.

The production of businesss equipment rose 0.6 percent in September, below the 1 percent increases of June and August and the 1.1 percent July business equipment increased 9.3 percent.

Since consumer demand slowed in the spring and summer, business investment has picked up the slack to keep the economy expanding. Consumer buying has shown signs of a resurgence in recent weeks.

Output of materials, such as steel, rose 0.8 percent despite limits on coal production because of the rail strike.

In another development, the Federal Reserve said that the nation's factories operated at about 85 percent of capacity in September, up slightly from the 84.9 percent rate recorded in August.