Hello Everyone
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

1/10 = (7/10)^n

n = log(1/10) / log(7/10) = ~6.45

if x^n = y, then n = log(y) / log(x)

n
1.00: 300
2.00: 210
3.00: 147
4.00: 103
5.00: 072
6.00: 050
6.45: 018
-----------
total: 900

Thank you for your help again, I didn't realise you introduced logs on the previous equation. however, I'm still little bit lost how you got the remaining sequence to get 900.
on this sequence , I thought using a geometric progression formula,subtituting the values you should get a whole number or nearest to the whole number ? and i'm not sure how you getting nth items to have decimal of two zeros. sorry, i think i have lots to learn . thanks

Sorry CEE; used .00 only to "keep columns at same width"!

This would have been clearer (2nd column = term amount, 3rd column = "so far"):
n
1: 300 : 300
2: 210 : 510
3: 147 : 657
4: 103 : 760
5: 72 : 832
6: 50 : 882
7: 35 : 917

Now you can "see" that 900 happens in between 882 and 917,
or in between 6 and 7, thus the 6.45 solution.

Thanks a lot for your further explanation, apprieciate. NB , the question requires to calculate the total number of months, whole number. I'm not sure how can do that if 900 happens between 6 and 7? or missing something

Round up or down, I guess:
6: 50
6.45: ?
50 / 6 * 6.45 = 53.75 ; so 53 or 54, depending...

Originally Posted by DenisB
Round up or down, I guess:
6: 50
6.45: ?
50 / 6 * 6.45 = 53.75 ; so 53 or 54, depending...
Thank you, i get how you came to the conclusion .though based on the question , i think there's something misleading