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
[tex]a_{n} = a_{n-1} + a_{n-2}[/tex] (n has to be greater than 2)
or, equivalently
[tex]a_{n+2} = a_{n+1} + a_{n}[/tex]
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.
