A Washington man and woman accused of fatally shooting a storekeeper in the back during a daylight robbery of her optician shop in the historic Old Town section of Alexandria last summer yesterday pleaded guilty to first-degree murder.

The pleas, entered in separate proceedings, brought to a close the aftermath of businesswoman Carol Ann Dodd's violent death -- one of the 175 cases of murder involving a handgun carried out in the Washington area during 1980.

The defendant who yesterday acknowledged pulling the trigger in the holdup, 25-year-old Darryl Jinks, was immediately sentenced to life imprisonment by chief Circuit Court Judge Wiley R. Wright. Jinks also received a 30-year sentence for robbery, and a mandatory one-year sentence for using a firearm to commit a crime. Because Jinks pleaded guilty, no appeal is possible.

"I hope Jinks will never be paroled," Alexandria chief prosecutor John R. Kloch said after the proceedings. "The sentences satisfy the family, the ends of justice, and this community," he said. Kloch prosecuted both defendants.

Jinks' companion in the fatal incident, Gail Williams, 21, of 1413 Oates St. NE, also pleaded guilty to first-degree murder, but received a 20-year sentence, with 10 years of it suspended, from Circuit Judge Albert Grenadier. She also received a five-year prison term for robbery.

Williams had been expected to plead guilty this week to one of the charges, and then testify against Jinks next week at his scheduled trial, according to lawyers familiar with the case.

According to law enforcement officials, a tip from a concerned citizen last September led them to Williams, who was arrested at her home. Several days later, police arrested Jinks at the Fairfax County jail, where he was being held on an unrelated robbery charge.

The shooting of Dodd, a native Alexandrian who lived with her parents in the city's Del Ray section, was one of a number of violent Old Town incidents in the last two years. Last October, Time-Life Books executive Constance Mellon was found shot once in the head, her hands bound behind her, in the upstairs room of her small Old Town residence. No arrests have been made in that case.

Last March, Mark Chase Sawtelle, also a Time-Life employe, was shot and seriously wounded during a daylight robbery attempt near his office as he tried to enter his car. One man was convicted of assault in that case.

In 1978, socialite Donita Cutts was beaten and bound during an apparent robbery attempt and died from smoke inhalation after an intruder set fire to her house. No one has ever been charged in that incident.

According to official figures, the rate of burglaries and larcenies increased a dramatic 21 percent in Alexandria in 1979, a rate that was nearly double that of neighboring jurisdictions. Assaults rose by 14 percent, from 270 in 1978 to 310 in 1979, officials said. Figures for 1980 are not yet available.