WASHINGTON — The U.S. economy grew at a better-than-expected 3.5 percent annual rate from July through September, the government reported Thursday, the clearest sign yet that the deep recession that’s gripped the nation is over.

“The increase in real GDP in the third quarter primarily reflected positive contributions from personal consumption expenditures, exports, private inventory investment, federal government spending and residential fixed investment,” the Commerce Department said.

Economic growth was powered by a number of sources that are turning up after almost two years of dragging down the economy. The positive numbers followed four consecutive negative quarters, the first time that’s happened since just after World War II.

The economy had shrunk at a 6.4 percent annual rate in the first quarter of this year and at a 0.7 percent rate in the second quarter, so the third-quarter growth shows that recovery is gaining steam.

“The 2009 third-quarter GDP numbers are proof that the great recession is over and a recovery has begun, ” said Mark Zandi, the chief economist for forecaster Moody’s Economy.com. “Most of the growth was driven by (federal) stimulus.”

The government’s “Cash for Clunkers” program to boost auto sales, he said, accounted for about half of the third-quarter growth in the gross domestic product, the broadest measure of value of U.S. goods and services produced. The Bureau of Economic Analysis, which prepared the preliminary growth estimates, said motor vehicle sales added 1.66 percentage points to third-quarter growth.