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I need a certain type of formula?
I have an item which has an increasing price of 10% each time you buy one.
I need to find a formula to find the total cost of a certain number of items (any number)
The initial cost is 2000, so it increases by 200 each time.
The cost of 6 is 15000.
What is a formula that connects the two variables? (total cost and amount purchased)
1 Answer
- jbdeedsLv 58 years agoFavorite Answer
I believe you are talking about an arithmetic price increase -- where you add on 200 for each purchase. This is not really an ongoing 10% price increase, which would multiply by 1.1 for each purchase. The example of the cost of 6 confirms this. So your progression of total costs is:
Buy 1: 2000
Buy 2: 2000 + (2000 + 200)
Buy 3: 2000 + (2000 + 200) + (2000 + 2*200)
...
Buy n: 2000 + (2000 + 200) + (2000 + 2*200) + ...+ (2000 + (n-1)*200)
In the general sum, there are n occurences of 2000. If we collect these together and look at what remains, we see 200 is a common factor. So the sum can be written:
Buy n: 2000*n + 200(1 + 2 + 3 + ...(n-1))
To get a final closed form, we invoke the well-known formula for the sum of the integers from 1 to n-1. That value is n*(n-1)/2. So your final formula for the purchase of n items is:
2000* n + [200*(n*(n-1)/2].
For n = 1, this gives 2000.
For n = 6, this gives 12000 + 3000 = 15000
For n = 10, this gives 20000 + 200*10*9/2 = 29000, etc.
