Clash of Clans Mathematics: Arithmetic Progression & Geometric Progression

We can learn some mathematics from the popular game, Clash of Clans!

Lets look at the Building Cost and Production Rate of the Gold Mine.

Source: http://clashofclans.wikia.com/wiki/Gold_Mine

We see that the Build cost actually follows a geometric progression(approximately) as each time, the build cost approximately doubles.

The formula for the n-th term of a geometric progression is $\boxed{ar^{n-1}}$ , where a is the first term, and r is the common ratio.

The above formula works well for the first 2 terms, for example the second term is $300=150(2^{2-1})$ .

However, the Production Rate follows an arithmetic progression, as per level, the production rate increases by 200/hr.

The formula for the n-th term of an arithmetic progression is $\boxed{a+(n-1)d}$ , where a is the first term, and d is the common difference. The formula works for all the 5 levels: for instance at level 5 the production rate is $1000=200+(5-1)(200)$ .