find next in an index

Hi,
I am trying to find out how to get the next record according to a
particular index.
I have a table with a name field and a serial field.  The name field
isn't unique so I made an index on name(varchar) & serialno(bigserial).
I also have an index just on 'name'.  I am having trouble working out
the syntax for the query.

select * from table where name>='jack' and serialno!='2'
order by name,serialno;

I don't think this will work under all circumstances.

Any help appreciated. Thanks.