Answer
There are 21 mature pairs of rabbits after 7 months.
Work Step by Step
In order to determine the total number of pairs of rabbits after 7 months, we will have to substitute $n=1,2,3,4,5$ until we get mature pairs.
$a_{1}=1, (a_{n}$ is month n-1)
$a_{2}=1,$ ($a_{1}$ haven't matured yet)
We can see that $a_{2}$ have not matured yet, and so $a_{1}$ produce a pair.
$a_{3}=2=1+1,$
$a_{3}$ are not matured yet, and $a_{1}$ and $a_{2}$ produce a pair each. We see that $a_{n}=a_{n-1}+a_{n-2}$.
So, $a_{4}=3=1+2$
$a_{5}=a_{4}+a_{3}=2+3=5$
$a_{6}=a_{5}+a_{4}=5+3=8,$
$a_{7}=a_{6}+a_{5}=8+5=13,$
$a_{8}=a_{7}+a_{6}=13+8=21$
So, this is the total for the 7th month.
Therefore, we find that there are 21 mature pairs of rabbits after 7 months.
