Match each recursively defined sequence with its correct classification. The given recursion formula is valid for all positive integers $n.$

$a_1=2$;$a_{n_{+1}}=3a_n$

$a_1=1$;$a_{n_{+1}}=3a_n+2$

$a_1=2$;$a_{n+1}=a_n+3$

$a_1=3$;$a_{n_{+1}}=2a_n$