Stating that 1980 "is shaping up as a very challenging year for our company," Washington Post Co. Chairman Katharine Graham told stockholders yesterday that declining Newsweek magazine and Washington Post newspaper advertising business is beginning to reflect the reality of recession.

"In the past four weeks, the recession has sharply affected the forward bookings of advertising at Newsweek," Graham said in an address to the company's annual meeting of shareholders here.

In contrast with the early months of 1980, the magazine's bookings are running more than 150 pages behind the pace of last year, she added. During a relatively strong first quarter, Newsweek's domestic edition had published 730 pages compared with 700 a year earlier, a period during which Post Co. profits were down from last year.

"There has also been a fall-off in advertising in the past few weeks at The Washington Post -- particularly in classified," the Post Co. chairman said. wA softness in advertising business also was apparent earlier at the company's two other newpapers -- the Trenton (N.J.) Times and Everett (Wash.) Herald.

Graham said that the "least overall pressure at this point" in terms of a recessionary impact on company operations is in broadcasting. National ad bookings for the firm's television stations in Detroit, Hartford, Miami and Jacksonville are "running very substantially ahead of a year ago" while local ad bookings are static, Graham told several dozen stockholders.

Summing up, Graham said that "all I can really say on the outlook at this point is that if the serious recessionary conditions that some are forecasting come to pass, we will be affected accordingly. We are not likely to ride out a severe recession this year as well as we did in 1974 of 1975.

In her addess to stockholders and responses to some questions at the meeting, Graham emphasized that a major factor in the more severe pressure on profits this year is a heavy investment program "that should contribute to our growth in a major way in future years."

Among the specific projects she mentioned were:

The new monthly magazine, Inside Sports, launched a month ago and expected to reduct pretax profits by $8 million in 1980. More than 40 percent (500,000-plus copies) of the press run for the first edition was sold in the first week, with a newsstand volume exceeding the total average issue newsstand sales of Sports Illustrated and Sport magazine combined, she said.

A proposed magazine called Newsweek Focus, a test issue of which will be distributed in eight markets for sale on May 19. If successful, the magazine probably would be published six times a year. Each issue would focus on a single topic of interest; the test issue topic is "mysteries of the universe."

A new $14 million braodcasting complex for the company's station in Detroit, WDIV-TV. The Detroit city council is expected to approve construction next week, and ground-breaking is set for August.

The Washington Post's new suburban printing plant in Springfield, to be opened and printing part of the daily paper's press run in September. The $65 million plant comes "just barely in time," Graham added, because Washington Post circulation has grown by 45,000 daily (to more than 600,000) and 61,000 on Sundays in the last three years and "we simply do not have the press capacity to keep up with reader demand."

Asked about the Post Co.'s absence from the cable television business, Graham said it had been considered in the past and that in her opinion it is "a good business." But management stayed away from cable because of heavy capital requirements and the "political part" of the process in winning community cable franchises, Graham added.

At the same time, she indicated that the Post Co. is considering related ventures such as supplying programming and information for cable and other home entertainment systems.