Answer
it is an arithmetic sequence
$d=7$
$a_{n}=11+7\left( n-1\right) $
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:
$2\times \left( 4+7n\right) =\left( 4+7\left( n+1\right) \right) +\left( 4+7\left( n-1\right) \right) \Rightarrow 8+14n=4+7n+7+4+7n-7\Rightarrow 8+14n=8+14n$
So this is arithmetic sequence
$a_{n}=a+\left( n-1\right) d=a-d+nd=4+7n\Rightarrow d=7;a-d=4\Rightarrow a=11$
$a_{n}=11+7\left( n-1\right) $
