Answer:
There will be as many pairs as the value of the nth term of the Fibonacci sequence
Step-by-step explanation:
During a month, only those pairs of rabbits that were given birth the previous month dont produce their pair. For the month n you take the amount of pairs of the n-1 month (lets call it an-1) and we have to add the new pairs created, that were created for rabits given birth on the month n-2 or before (in other words, the active ones). This means that an-2 pairs were created, so the total number of pairs, an, is given by the formula
(n has to be greater than 2)
or, equivalently
This is Fibonacci's formula for values greater than 2, also note that
a1 = 1
a2 = 1 ( because the pair was inactive this month)
a3 = 2 (because now the pair is activa)
As a result, we have
a1 = 1
a2 = 1
an+2 = an+1 - an (with n at least 1)
Thus, there were as many pairs in the nth month as the value of the nth term in the Fibonacci sequence.