Given ( a_n = 4 + 3n )

( a_{n+1} ): [ a_{n+1} = 4 + 3(n+1) = 4 + 3n + 3 = 7 + 3n ]

( a_{2n} ): [ a_{2n} = 4 + 3(2n) = 4 + 6n ]

Answer: ( a_{n+1} = 7 + 3n ), ( a_{2n} = 4 + 6n )