The government reported on Thursday that the nation’s economic output rose at a 3,5% annual rate in the third quarter, offering a strong sign that the economy’s plodding growth may be picking up speed.

The higher-than-expected bump in gross domestic product — a measure of all the goods and services produced — was driven in part by an unusual spurt of federal spending, concentrated in defense, combined with robust exports and investment in business equipment.

“This is the strongest six-month interval we’ve had in 10 years,” said Carl R. Tannenbaum, chief economist at the Northern Trust Company. “The pace of the expansion has clearly increased.”

“I don’t think it’s going to be hard to maintain a growth of 3% for the fourth quarter,” he added, echoing several other forecasters.

The performance of the economy during the summer months of July, August and September followed the second quarter’s even more impressive 4,6% annualized growth rate. This sustained expansion was welcomed after a bitter winter that contributed to a disappointing 2.1% decrease for the first three months of the year.

But the enthusiasm was tempered. John Canally, chief economic strategist for LPL Financial, called the latest gross domestic product figures confirmation that “we’re doing O.K. here.”

That was also the conclusion voiced on Wednesday by the Federal Reserve, which cited a strengthening labor market and decreasing concerns about the slow pace of inflation as reasons to close the books on its six-year, multitrillion-dollar bond-buying spree.

Government statisticians will revise Thursday’s figure twice, first in November and then in December. Thus, the final measure of growth could end up being restated by as much as a percentage point in either direction, according to Pantheon Macroeconomics.

There were caveats, of course. Consumer spending, though up 1,8%, was weaker than some economists had expected, given recent job growth, falling gas prices and profits that wealthier households reeled in from the stock market.

“The components may not be as strong as the headline number shows,” said Krishna Memani, chief investment officer at Oppenheimer Funds. The housing sector was also weaker than some economists had hoped.

Military spending, which rose a whopping 16%, is notoriously volatile, seesawing from one quarter to the next. Still, for nearly two years, government austerity has been a drag on the economy, and the 10% growth in federal spending reversed that trend, at least for one quarter.

Many economists are worried about the effect of Europe’s anemic growth on the American economy, expressing fears that European policy makers and the European Central Bank are not doing enough to stimulate their sluggish economies. An announcement by the European Central Bank on Monday that it was buying 1.7 billion euros’ worth of private assets was dismissed by some economists as too piddling an effort given the region’s economic problems.

And in a speech in Boston this month, Janet L. Yellen, the Fed chairwoman, expressed concern about a decline in the number of new businesses, which are traditionally a vehicle for enterprising Americans to get ahead. Lurking beneath all the statistics is the insistent worry that even the most promising numbers are masking profound inequalities and stagnant incomes for most Americans, as Ms. Yellen indicated in her Boston speech.

“It is no secret that the past few decades of widening inequality can be summed up as significant income and wealth gains for those at the very top and stagnant living standards for the majority,” she said. “I think it is appropriate to ask whether this trend is compatible with values rooted in our nation’s history, among them the high value Americans have traditionally placed on equality of opportunity.”

All in all, though, this week handed the optimists considerable ammunition. The Labor Department Said on Thurssday that new claims for unemployment insurance benefits remained at recent low levels. The four-week moving average was 281,000, compared with 352,500 a year ago.

And a report from the Conference Board showed that the consumer confidence index leapt in October to a seven-year high. That upbeat outlook combined with falling gasoline prices could help push consumers to open their wallets even more during the coming holiday season.

Steven Blitz, chief economist at ITG Investment Research, was less sanguine about reaching 3 percent growth — the economy’s average growth rate in the postwar era — than he was about the underlying causes. He cited the increase in exports and fixed investments as a good sign that the economy was evolving toward more domestic production.

“That’s a more realistic building block for the economy than to have overleveraged consumers buying homes,” he said.