Two ways to get the end of the previous month:
Select eomonth(getdate(), -1)
, dateadd(month, datediff(month, -1, getdate()) - 1, -1)
If the data type of the column EntryDate is a date data type - then EOMONTH would be a better option as it returns a date. If the columns data type is datetime, then the second option would be better as it returns a datetime.
With that said - are you certain you will always have a row on the last day of the month for every member? If not, and you want the latest row available in that month for each member - then it becomes a bit more challenging. If that is the case, let us know and we can provide a different solution.
Note: no reason to use DISTINCT - unless you know there could be duplicate values in the results.
Final question: do you want the row with the highest value returned - or just the highest value in that column? If you want the row - then you need to look at row_number() function, something like rn = ROW_NUMBER() OVER(Partition By MemberNumber Order By AccountSequenceNumber DESC).
Put the query in a CTE or derived table and select from the CTE/derived table where rn = 1.