The Big Three domestic automakers started the 1982 model year on an unusually sour note, with early October sales dropping a sharp 34.7 percent from the same period last year.

The seasonally adjusted annual rate of sales was only 4.8 million, the lowest in a devastating auto industry slump that has continued since April 1979.

Sales for the Big Three automakers during Oct. 1-10 were 141,437, down from 216,462 in the same period last year.

Ford Motor Co. reported it sold 34,618 domestic cars in the period, down 43.3 percent from 61,029 in early October of last year. General Motors Corp. reported sales of 86,887 cars, down 31.9 percent from 127,573 last year. Chrysler Corp. said it sold 19,932 cars, down 28.5 percent from 27,860.

Among other automakers, Volkswagen of America reported that its sales of U.S.-built Rabbit sedans were down 7.7 percent to 2,529. American Motors Corp. sales were estimated to be down 23.1 percent to 3,100. AMC reports sales only at the end of the month.

For the year so far, Chrysler domestic car sales remain 19.7 percent ahead of last year at 599,757. Ford sales for the year are down 0.8 percent from last year to 1.1 million and GM is down 3.5 percent to 3 million.

Also for the year, Volkswagen of America is off 11.7 percent to 128,759, and AMC has declined 3.9 percent to an estimated 112,975.

Chrysler announced today that it would offer a "Chrysler Savings Certificate" worth $300 to $1,000 to customers who buy certain 1981 and 1982 cars or trucks from participating dealers. The offer began today on all cars delivered before the end of the year.

It touched off a price-cutting binge earlier when it held prices at 1981 levels on some 1982 cars. GM and Ford then jumped in with financing-rate discounts and rebates.