Universal Analytics Metrics

7 Day Active Users is a Metric in Google Analytics under the User section

7 Day Active Users Definition: Total number of 7-day active users for each day in the requested time period. At least one of ga:nthDay, ga:date, or ga:day must be specified as a dimension to query this metric. For a given date, the returned value will be the total number of unique users for the 7-day period ending on the given date.