A rabbit covers a certain distance in such a way that he covers one-fifth of the distance covered on the previous day. If he covers 12000 meters on the first day, what is the maximum possible combined distance he can travel for all the days?

The Rabbit covers the distance in a geometric progression, with common ratio i.e 'r'= 1/5.

Since it travelled 12000 meters on the first day, the first term of the series is 12000

Now, we know that $$0<r<1$$ and in that case, the geometric progression is infinite. 

Hence, maximum distance it can cover = Sum of infinite GP= $$\dfrac{\ a}{1-r}$$, where a = 12000 and r = 1/5

So, combined maximum distance the rabbit can travel on all the days = $$\dfrac{12000}{1-\dfrac{1}{5}}\ =\ \dfrac{12000}{\dfrac{4}{5}}=12000\times\dfrac{5}{4}=15000$$ meters