Hello Everyone

Please help with geometric sequence problem:

A machine that produces an item that is being phased out will be disposed immediately after the last order of 900 parts is completed.The machine's monthly production is as follows : 300,210,147...How many months of production is needed in order to hire a part time worker.bear in mind that the machine's life has nearly come to an end where further maintenance costs are not necessary and too costly

I have tried to solve it as follows; from geometric series given 210 dived by 300= 7/10 therefore the common difference is 7/10

From geometric series sum formula S= a(r^n-1)/r-1, therefore 900=300(7/10^n-1)/ 0.7-1 which led me to 1/10=(7/10)^n. i can't solve it any further . please help where am getting it wrong