Translating regular wording into a mathematical expression

Question

Given a product that initially costs $2000$ dollars and will cost $200$ dollars more on each subsequent purchase (for example a total of $6600$ spent on the third purchase), how would I write a function to calculate the TOTAL cost of purchasing the product $x$ amount of times?

Answer 1

We can find the total cost y for x amount of purchases of this product using the formula for the sum of an arithmetic progression:

$$y=\frac{x}{2}(2a+(x-1)d)$$

where a equals the initial price of 2000 dollars
where d equals the common difference of 200 dollars