You have the following sequence for the population of the rabbits:
6, 18, 54, ...
The explicit formula for the previous sequence is obtained by considering the values of n (1,2,3,..) for the first terms of the sequence.
You can observe that the explicit formula is:
a(n) = 6·3^(n - 1)
in fact, for n=1,2,3 the result is:
a(1) = 6·3^(1 - 1) = 6·3^0 = 6
a(2) = 6·3^(2 - 1) = 6·3^1 = 18
a(3) = 6·3^(3 - 1) = 6·3^2 = 6·9 = 54
which is consistent with the given sequence 6, 18, 54, ...
