It can be tricky to really know how much it costs to buy something like 100+ of one type of path because it always increases. Sometimes you end up paying double or triple the amount for the last one than you did the first. To figure out beforehand how many coins you need to buy all your decorations use this formula.

I believe all the decoration that do increase in price each time you buy one increase by the same amount each time. If it doesn’t increase by the same amount each time then this formula won’t apply

variables (to make it easier to see)

a=#of decorations of a certain type you are buying

c=change in price each time you buy that decoration

b=the price of the decoration currently in your shop

d=product of (a-1) and c

e=quotient of d divided by 2

f=sum of b and e

p=final price

Formula: a{[(a-1)(c)]/2+b} or (1/2ca*2)-(1/2ca)+(ba)

a*2= a(a)

I’ll use the first formula to break down how it works since it is easier to explain, but either works! The second formula is the simplified form and the first one is the factored form.

Breakdown:

First multiple (a-1) and c: This finds the amount of change in price between the first and last decoration.

(a-1)(c)=d

Next divide d by 2: This finds the average change in price from the base price.

d/2=e

Add e to b: This finds the average cost of one decoration.

e+b=f

Lastly multiply f by a: This multiplies the average price of one decoration by the number being bought to give a total amount.

a(f)=p

Example: I want to buy 100 paths that increase by 12 each time and my shop price is 360.

(100-1)(12)=1200-12=1188

1188/2=594

594+360=954

954(100)=95400

Feel free to ask for any questions or further examples if needed!