Answer
After 7 months there are 21 mature pairs of rabbits.
Work Step by Step
$a_{1}=1, (a_{n}$ is month n-1)
$a_{2}=1,$ ($a_{1}$ haven't matured yet)
$a_{3}=2=1+1,$ ($a_{2}$ haven't matured yet, $a_{1}$ produce a pair)
$a_{4}=3=1+2,$
($a_{3}$ havent matured yet, $a_{1}$ and $a_{2}$ produce a pair each)
... note that, so far, $a_{n}=a_{n-1}+a_{n-2}$ as the hint suggests.
$a_{5}=a_{4}+a_{3}=2+3=5$
$a_{6}=a_{5}+a_{4}=5+3=8,$
$a_{7}=a_{6}+a_{5}=8+5=13,$
$a_{8}=a_{7}+a_{6}=13+8=21$ (this is the 7th month total)
After 7 months there are 21 mature pairs of rabbits.
