The real estate data provider also said Tuesday that prices declined 0.3 percent in September from August, the first drop after six straight increases. The monthly figures are not seasonally adjusted. CoreLogic says the monthly decline reflects the end of the summer home-buying season and not a softening in the housing recovery.

Steady price increases should give the housing market more momentum when home sales pick up in the spring. Rising prices encourage more homeowners to sell their homes and entice would-be buyers to purchase homes before prices rise further.

Other measures have also shown healthy gains in home prices over the past year. The Standard & Poor’s/Case Shiller 20-city index rose 2 percent in August compared with a year ago, a faster pace than the previous month.

The price gains in the past year reported by CoreLogic were widespread. Prices have risen in all but seven states. And they declined in only 18 out of 100 large cities that are tracked by the index.

Some of the biggest increases were in states that suffered the worst from the housing bust. Home prices in Arizona jumped 18.7 percent in the past year, the most of any state. Home prices in Idaho rose 13.1 percent, the second largest. Nevada’s home values rose 11 percent.

Home prices jumped 22.1 percent in Phoenix, the metro area with the biggest gain. Prices in Houston rose 6.6 percent, the second-highest increase.

The states with the biggest drops were Rhode Island (3.5 percent) and Illinois (2.3 percent).

CoreLogic’s price index is based on repeat sales of the same homes and tracks their price changes over time.

Several reports last month showed that the housing market is improving, though from depressed levels.

Home builders started construction on new homes and apartments at the fastest pace in more than four years in September. They also requested the most building permits in four years, a sign that many are confident that home sales gains will continue.

New home sales jumped last month to the highest annual pace in the past two and a half years. Sales of previously occupied homes dipped in September but have risen steadily in the past year.

Sales of both new and previously occupied homes are still below levels that are consistent with a healthy housing market. That’s partly because the supply of available homes for sale remains low. And many prospective home buyers are struggling to qualify for a mortgage or scrape together the bigger down payments that many banks are requiring.

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By Christopher S. Rugaber