Select a recursive definition with initial condition$($s$)$ for the following sequence $\{an\}.$ For $n=1,2,3,$dots

$a_n=n(n+1)$

$a_1=2$ and $a_{n+1}=a_n+4$ for all $n1.$

$a_1=1$ and $a_n=a_{n-1}+2n-1.$

$a_1=0,a_2=2,$ and $a_n=a_{n-2}$ for all $n3.$

$a_1=2$ and $a_n=a_{n-1}+2n$