$A.\phantom{\rule{1em}{0ex}}{N}_{1}=10,{N}_{k}=10{N}_{k-1}$

$B.\phantom{\rule{1em}{0ex}}{N}_{1}=10,{N}_{k}=14{N}_{k-1}$

$C.\phantom{\rule{1em}{0ex}}{N}_{1}=10,{N}_{2}=100,{N}_{k}=10{N}_{k-1}+40{N}_{k-2}$

$D.\phantom{\rule{1em}{0ex}}{N}_{1}=10,{N}_{2}=140,{N}_{k}=14{N}_{k-1}+40{N}_{k-2}$

$E.\phantom{\rule{1em}{0ex}}{N}_{1}=14,{N}_{2}=196,{N}_{k}=10{N}_{k-1}+14{N}_{k-2}$

Regardless of the choices, how can one deduce the recursive formula?