The number of homes in some state of foreclosures in the New York City area jumped by 34 percent for the first quarter compared to last year, according to a report by RealtyTrac, an online real-estate service. In Brooklyn, one out of every 241 homeowners is facing foreclosure, more than double the rate from a year ago. The metro area ranks No. 80 for foreclosures among the nation’s top 100 regions. Westchester County has seen a 138 percent increase this year. Staten Island saw a 101 percent increase, while Manhattan’s foreclosures increased 66 percent and Queens’ 41 percent.