Sales of insurance by Geico Corp. increased 30 percent, helping the District firm raise its earnings 195 percent in the first quarter, the company said yesterday.

Chairman John J. Byrne, in his assessment of Geico's performance in 1982, said the firm "did not attract as many new customers as we should have," contributing to a 41 percent decline in profits over 1982.

But the first-quarter figures posted yesterday show Geico rebounding, earning $49.8 million ($2.35), compared with $16.9 million (82 cents) in the first quarter of 1982.

The 1983 numbers include a realized investment gain of $28.9 million from the sale of securities, significantly higher than the $1.2 million realized investment gain in the similar period last year.

"The year is off to a reasonably good start. Our first quarter earnings were up nicely--a better percentage increase than we expect to develop for the full year," Byrne said in a statement yesterday. "Sales to new customers are up 30 percent," he said.

Washington-based Syscon Corp., an electronics systems engineering and energy planning group, reported a 30.3 percent increase in earnings, up to $689,000 (26 cents) from $440,000 (16 cents) in the year-ago quarter.

Syscon's sales were $18.8 million, a 15 percent increase over $16.4 million earned in the first quarter of 1982.

At Hazleton Laboratories Corp. in Vienna, nine-month revenue climbed to $52.1 million from $39 million, but profits declined slightly to $2.3 million (63 cents) from $2.4 million.

In the latest quarter, the biological and chemical research company earned $473,000 (13 cents), compared with $810,000 (23 cents) in the third quarter last year. Revenue increased to $18.1 million from $15.1 million

Springfield-based Logetronics Inc., a computer company specializing in image processing, lost $529,000 (39 cents a share) in the first quarter of 1983, compared with a net income of $213,000 (16 cents) in the year-ago quarter.

Logetronics sales were down 33.6 percent, a drop to $7.5 million from $11.4 million last year.

Reston-based Scope Inc., an electronics manufacturing company, reported a first-quarter loss of $360,000 (30 cents), compared with a loss of $251,000 (21 cents) in the year-ago period.

Scope's sales dropped 24.5 percent, down to $2.0 million for the quarter from $2.6 million last year.