U.S. home prices dipped in January for the third straight month, likely because of slower sales in recent months caused by cold weather, a limited supply of homes and higher mortgage rates.The Standard & Poor’s/Case-Shiller 20-city home price index, released Tuesday, declined 0.1 percent from December to January, the same drop as the previous two months.In Dallas-Fort Worth, the index declined by 0.2 percent. That figure is not adjusted for seasonal variations, so the dip partly reflects weaker winter sales. The index rose a healthy 13.2 percent in January from 12 months earlier. But that is down from a 13.4 percent increase in 2013 and is the second straight decrease. North Texas home prices were up 10 percent from January 2013.Most economists aren’t concerned about the moderation in price gains. Home prices jumped over the past two years as very low mortgage rates pushed up sales. And the supply of available homes remained tight. Many homeowners couldn’t sell because they owe more on their mortgages than their houses are worth. Meanwhile, investors swooped in and bid up prices in places like Las Vegas, Phoenix and other cities in the South and West. “The home price appreciation we’ve been seeing is unsustainable,” said Stan Humphries, chief economist at real estate data provider Zillow. “It needs to moderate over time or we risk inflating another housing bubble.” The Case-Shiller index covers roughly half of U.S. homes. The index measures prices compared with those in January 2000 and creates a three-month moving average. The January figures are the latest available. Twelve cities reported price declines in January from the previous month. The biggest decline was in Chicago, where home prices dropped 1.2 percent, followed by Seattle, where prices fell 0.8 percent. Las Vegas reported the biggest price gain, up 1.1 percent, followed by Miami, with 0.7 percent. Compared with a year earlier, New York and Washington, D.C., posted their largest gains since 2006, just before the housing bubble burst. The slowdown in price gains follows other signs that the housing recovery has hit a rough patch. Sales of existing homes in February fell to their lowest since July 2012. And home construction slipped for the third month in a row, though builders sought more permits in February than in any month in four years. Mortgage rates are roughly a full percentage point higher than they were last spring, but they remain low by historical standards. The average rate on the 30-year loan is 4.32 percent, mortgage buyer Freddie Mac said last week, down from 4.37 percent the previous week. Most economists expect home sales and prices to rise in 2014, particularly as the weather improves, but more slowly.