Consider the case of non level monthly deposits as follow :

a) The deposits $ 100 will be paid regularly every three months period, where its starting right now, the second deposit takes place at the end of month 3 rd, and so on until it reached and stopped at the end of month 30th .

b) The deposits will be paid regularly every two months period, whose the first deposit $ 200 is paid at the end of month 1 st, then the subsequent deposits decrease by $ 10 each twice month are paid at the end of month 3 rd , month 5 th , and so on until the deposit amount reaches $ 50 (the deposits remain $ 50 thereafter) up to a maximum month 40th period.

However, I need to withdraw certain amount of money periodically (monthly), whose initial withdrawal is $ X, and the next withdrawal are $ 2X, $ 3X, (so on). The monthly withdrawal ($ X, $ 2X, $ 3X, $ 4X, $ 5X) started from the end of month 36th until the end of month 40th, such that the remaining balance becomes exhausted (zero balance) at the end of month 40th . Those deposits and withdrawals are credited with = 8% annualy, where it remains unchanged forever. Calculate $ X. Show your work and prove every detail.