Sherri Lynn Goff didn't hesitate to let her older brother use her car when he asked to borrow it in February. But she was surprised when he called a few hours later with news that her 1978 Mercury Bobcat had been stolen from a grocery store parking lot.

"He had left the keys in it," Goff, 24, said yesterday. "He apologized 100 times. I even felt sorry for him. But it was just carelessness."

Similar forgetfulness is partly responsible for an alarming increase in car theft throughout the Washington area, according to police. The increase is particularly dramatic in Montgomery and Prince George's counties, according to crime statistics released this week.

In Montgomery, police noted a 47 percent increase in auto theft reports in the first three months of this year compared with the same period of 1985. Prince George's police said that in the first seven weeks of the year an average of 23 cars were reported stolen each day. The number of stolen cars this year totals 1,097, according to police. If the rate continues, police said, almost 8,400 car thefts would be reported by year's end, an increase of 40 percent over 1985.

Police said they are not sure what is causing the sharp increases in auto theft.

"It looks like it will be more of the same, the way reports are coming in this year," said Sgt. Ray Daniels, head of the Prince George's County police car theft unit. "Anyplace a vehicle sits for an extended period of time, like a shopping center or apartment parking lots, it's subject to get stolen. Day or night, it doesn't matter anymore."

Other jurisdictions in the Washington area reported car theft increases last year. In the District, car theft was up 14.9 percent in 1985 compared with 1984, with 5,024 car thefts reported last year. In Arlington County, according to Virginia State Police, auto theft in- creased 13.8 percent in 1985 from 1984. In Fairfax County, there was a 13.8 percent increase in the number of stolen cars, and in Alexandria auto theft was up 5 percent in 1985 over the previous year.

Daniels, of Prince George's, said there is no single explanation for the increase in car thefts.

More people are stealing cars, he said, and more people are stealing more than one of them. He said that about 15 percent of the cars are recovered. The worst season for car thefts is usually summer, Daniels said.

When Prince George's police found Jerry Dunlop, 18, of Largo driving an apparently stolen Datsun into the parking lot of the Penn Mar Shopping Center in Forestville, according to court records, an officer watched Dunlop get out of the Datsun and start "tampering with a second car." Police confiscated a screwdriver when they charged Dunlop with car theft, according to court records.

And then there are car owners who make it easy for thieves to take their vehicles by leaving doors unlocked or keys in the ignition. "About 80 percent of the cars stolen were either unlocked or had keys in them," Daniels said. "The rest are taken by a determined person. If a person wants your car, he's going to get it."

To better protect cars, Daniels suggests, owners should avoid leaving cars parked in the same spot for long periods and should try to park in lighted areas. Most of all, he said, drivers should take their keys and lock their cars when they are unattended.