Time Inc. reported record revenues and earnings for the first quarter yesterday, and the company's board of directors approved a 15 percent increase in the quarterly dividend to 37 1/2 cents a share.

Time shareholders, who gathered at the Time-Life Building for the annual meeting, were told that revenues in the first quarter rose to $345.5 million, 28 percent above the same quarter last year. Net income rose to 39 percent to $21 million ($1.03 a share).

There was unusually tight security at the meeting, reminiscent of annual meetings during the Vietnam War protests. The Credentials of stockholders and reporters were scrutinized, a shareholders had to pass through a metal detector before entering the meeting room.

According to a Time spokesman, the tight security was suggested to the company by the New York Police Department after Time reported that its personnel had received threatening letters.

The spokeman said the letters came from "symphathizers of Synanon," the drug rehabilitation program that has filed a $27 million suit agaisnt Time magazine charging it with libel and religious persecution.

Time shareholders entering the building passed by some 250 Syanon protesters denouncing the magazine and distributing leaflets.

During the meeting, shareholders sympathetic to Syanon insistently questioned Time Chairman Andrew Heiskell about the company's editorial and financial policies.

In his address to shareholders, Time President James R. Shepley, apparently referring to the threatening letters, said that "a new and sinister scourge threatens publishers and journalists. That scourge is violence, even terrorism." Noting that several editors and reporters had been murdered in recent years, he added: "I am certain we at Time will not be frightened by menace from either left or right."

All this was in dramatic contrast to Shepley's bright report on the company's finances. Among other things, he said that over the past 5 years Time had grown at a compound rate of more than 18 percent. He noted that the rate of return on stockholders' equity exceeded 15 percent in 1977, the highest in ten years.

Shepley did not make any disclosures about the company's plan for The Washington Star, which it acquired earlier this year. One stockholder from Washington asked if the acquisition of The Star and the move last year of Time-Life books to Alexandria indicated of a trend. "We've moved as much in your direction as we will," responded Heiskell.

Shepley said all the company's magazines will raise subscription prices by mid-year in order to keep pace with the continuing rise in postal rates.

The video group, which became with the most of what Mr. Williams says."

But Williams views the whole free profitable for the first time last year, was described by Shepley as the company's "fastest growing business. It includes Time-Life films, Home Box Office pay-tv, Manhattan Cable TV and WOTV an NBC-affiliate in Grand Rapids, Mich.

Last month, Time's board approved the acquisition of American Television and Communication Corp., the second largest owner of cable TV stations in the country, which is based in Denver. Shepley predicted the deal should be completed later this year. But he added, "the acquisition requires Federal Communication Commission approval and is currently under scrutiny by the Justice Department."

The third major acquisition by Time in the past 12 months was the Book-Of-The-Month-Club.