We can rewrite the given values as
[tex]\begin{gathered} \ln (2)=\ln (2^1)=1\times\ln (2) \\ \ln (4)=\ln (2^2)=2\times\ln (2) \\ \ln (8)=\ln (2^3)=3\times\ln (2) \\ \ln (16)=\ln (2^4)=4\times\ln (2) \end{gathered}[/tex]
Then, the common difference is ln(2). For instance,
[tex]\ln (2)-\ln (4)=1\times\ln (2)-2\times\ln (2)=-\ln (2)[/tex]
Therefore, the answer is: Yes, the sequence is arithmetic with common difference d:
[tex]d=-\ln (2)[/tex]
