Answer
sequence is not arithmetic
Work Step by Step
İn order a sequence to be arithmetic :
$a_{n+1}-a_{n}=a_{n}-a_{n-1}\Rightarrow 2a_{n}=a_{n+1}+a_{n-1}$
So:
$a_{n+1}+a_{n-1}=4+2^{n+1}+4+2^{n-1}=8+2^{n+1}+2^{n-1}$
$2a_{n}=2\left( 4+2^{n}\right) =8+2^{n+1}$
As we see from above
$a_{n+1}+a_{n-1}\neq 2a_{n}$
So this sequence is not arithmetic