Home prices increased in September in most major U.S. cities, more evidence of a housing recovery that is providing a lift to the fragile economy.

The Standard & Poor's/Case Shiller national index measuring prices in 20 cities rose 3 percent in September compared with the same month a year ago. Prices also gained 3.6 percent in the July-September quarter compared with the same quarter in 2011.

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Across the nation, prices increased in 18 of 20 cities. Phoenix prices jumped 20.4 percent over that stretch to lead all cities. Prices in Atlanta showed a modest 0.1 percent increase, ending 26 straight consecutive year-over-year declines.

Prices also rose in September from August in 13 cities. Five metro regions, including New York, posted declines, and two were unchanged. Monthly prices are not seasonally adjusted.