WASHINGTON — A summer of modest economic growth is helping dispel lingering fears that another recession might be near.

Whether the strength can be sustained is less certain.

The economy grew at an annual rate of 2.5 percent in the July-September quarter, the Commerce Department said Thursday. But the growth was fueled by Americans who spent more while earning less and by businesses that invested in machines and computers, not workers.

The expansion, the best quarterly growth in a year, came as a relief after anemic growth in the first half of the year and weeks of wild stock market shifts.

The economy would have to grow at nearly double the third-quarter pace to make a dent in the unemployment rate, which has stayed near 9 percent since the recession officially ended more than two years ago.

For now, the report on U.S. gross domestic product, or GDP, sketched a more optimistic picture for an economy that only two months ago seemed at risk of another recession.

And it came on the same day that European leaders announced a deal in which banks would take 50 percent losses on Greek debt and raise new capital to protect against defaults on sovereign debt.

Stocks surged on the European deal and maintained their gains after the report on U.S. growth was released. The Dow Jones rose 340 points to close at 12,209. The Dow hadn’t closed above 12,000 since Aug. 1. The Standard & Poor’s 500 index is close to having its best month since 1974.

The GDP report measures the country’s total output of goods and services. It covers everything from bicycles to battleships, as well as services such as haircuts and doctor’s visits.