Answer
It is an arithmetic sequence.
$d=\ln2$
Work Step by Step
A sequence is arithmetic if $a_2−a_1=a_3−a_2=a_4−a_3=a_5−a_4=...=d$
For the given sequence we have that:
$a_2-a_1=\ln2-\ln1=\ln(\frac{2}{1})=\ln2$
$a_3-a_2=\ln4-\ln2=\ln(\frac{4}{2})=\ln2$
$a_4-a_3=\ln8-\ln4=\ln(\frac{8}{4})=\ln2$
$a_5-a_4=\ln16-\ln8=\ln(\frac{16}{8})=\ln2$
It is an arithmetic sequence.
Common difference: $d=\ln2$
