# 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 , 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 .

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 , 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 .

Thanks for reading, and do “like” this post if you enjoy reading it! Hope you learnt some mathematics along the way.

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