SOLUTION: So what I really need is the formula to use here. I can figure out the answer but would like the formula for different numbers. I have $150,000,000 and planning on purchasing a

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Question 316907: So what I really need is the formula to use here. I can figure out the answer but would like the formula for different numbers.
I have $150,000,000 and planning on purchasing an item that costs $200,000. I can only buy one at a time and every time I purchase this item the price increases by $1,800. How many times can I purchase this item?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
You have an arithmetic progression with a starting value of 200000 and a difference of 1800.
An=200000%2B1800%2A%28n-1%29, with n=1,2,3,...
The sum of an arithmetic progression is given as,
Sn=%281%2F2%29%282A1%2Bd%28n-1%29%29n
%281%2F2%29%282%28200000%29%2B1800%28n-1%29%29n=150000000
400000n%2B1800n%28n-1%29=300000000
400000n%2B1800n%5E2-1800n=300000000
1800n%5E2%2B398200-300000000=0
18n%5E2%2B3982n-3000000=0
9n%5E2%2B1991n-1500000=0
Using the quadratic equation,
N=312.6
You will be able to buy the 312th item but won't have enough money left for the next item.