From Dr. Sarah Sargent (with edits)
There seems to be some contradiction in records whether the father of Andrew (1597-1629) is John Sargent (1566-1614), or William Sargent (1572-1601), vicar of Meare, Somerset.
Whilst geography is of course not the sole factor in sorting out genealogy, it seems a bit improbable for John Sargent to have moved around from Northamptonshire to the West of England and then to the North of England in a very few short years, having children as he went...
More sensible from a geographic viewpoint would be that the William Sargent, vicar of Meare, Somerset, was the father of Andrew. There seems to be some confusion on the dates of birth and death for this William Sargent, but having done some careful searching, I did come up with this record from the Clergy of the Church of England database, showing that he was appointed as a vicar in Meare, Somerset, on November 11, 1599. http://ccedb.cch.kcl.ac.uk/jsp/DisplayAppointment.jsp?CDBAppRedID=132277
From the records, it would appear he died before March 27, 1601, this being the date the next vicar was installed. I have seen some dates on the internet that give his date of death as March 2, 1601. http://www.somersetlarders.com/localhistory/history_local_meare_incumbents.html
Also shows William Sargent as the vicar at St Mary's Meare.
Andrew Sargent 1597-1629 (married Mary Wathen or Walten)
William Sargent (1624-1715) (married Abigail Clark) (this being apparently the person who emigrated from England to the colony of Gloucester in Massachusetts)
William Sargent (married Hannah Short)