Since during middle of each month, Bryce withdraws half of his amount. So at the end of each month, his balance is 1/2 times as compared to balance of his previous month.
The following recursive function represents the Brye's balance at end of each month:
where
is the account balance of previous month. And 
is the account balance of current month.
The following recursive function represents the Brye's balance at end of each month:
where