Industrial production increased sharply in April for the third consecutive month, the Federal Reserve Board reported yesterday.

The nation's central bank said that the output of the nation's factories, mines and utilities grew 0.8 per cent in April. Production increased 1.4 per cent in March, partly reflecting a catchup in production after the bad weather and fuel shortage in January and early February.

Industrial output fell 0.8 per cent in January, but by February the nation's factories had overcome much of the problems associated with gas shortages and cold weather. According to revised figures, production jumped 0.8 per cent in February, the same as in April.

Aside from a decline in automobile producton, which had surged in March, "relatively large gains in output were widespread in April," the Federal Reserve Board said.

The agency reported that automobiles were put together at an annual rate of 9.3 million units in April, 4 per cent below the March rate. The Fed cited strikes at some plants as well as a cutback in production because automakers are overstocked with some small model cars.

The Fed's index of industrial production stood at 136.1 per cent of its 1967 average, 6 per cent higher than in April 1976 and 3 per cent above June 1974, the highest level it reached before the severe recession of later 1974 and 1975. In April alone, production increased at a compound annual rate of 10 per cent.

Aside from the slight decline in automobile production, output of "of other consumer durable goods continued to advance strongly and output of nondurable consumer goods (such as clothing and foods) picked up."

There was a 0.8 per cent increase in business equipment in April following a 1.1 per cent advance in March.

Iron and steel production rose sharply for the third straight month.

In another development, the Commerce Department reported that business inventories increased 0.9 per cent in March. Businesses added $2.8 billion to their stocks in March after adding $2 billion in February.

Increasing inventories - business stocks rose $2.6 billion in the final months of 1976 compared with $7.7 billion in the first three months of 1977 - contributed to increasing industrial production.