Overview
Want to know how to calculate how much a certain level of province defense will cost you? It’s really easy with this quick trick.
Province Defense Cost Basics
The guide says that each new level of province defense costs gold equal to that new level. So the first level costs one gold. Each level after costs the number of PD, so 2 PD is 2 gold and so on. To solve for PD of 10 it would be: 1+2+3+4+5+6+7+8+9+10 = 55. Quickly adding more than 10 or so becomes a pain. Turns out there is a better way.
A Better Way
Turns out that the progression of the PD costs is an example of an arithmetic series[en.wikipedia.org]. This means that if we know the first and last number of the series and how many numbers are in the series we can quickly find the sum. The first number is 1. The last is whatever max value of PD you want. How many numbers in the series is also the max value of the PD.
Once you have those three values:
- Add the first and max value together (1 + 10 = 11)
- Multiply that by how many numbers in the number ( 11 * 10 = 110)
- Divide that by 2 to get your answer (110 / 2 = 55)
It’s that easy. With this we can easily figure out even large PD values like 35.
35+1 = 36
36*35 = 1,260
1260/2 = 630
I hope this helps make figuring out your master plans a little easier. =)