The nth term of a sequence is given by an

We have:

$a_{n}=2 n^{2}+n+1$

$a_{1}=2 \times 1^{2}+1+1$

= 4

$a_{2}=2 \times 2^{2}+2+1$

=11

$a_{3}=2 \times 3^{2}+3+1$

=22

$a_{2}-a_{1}=11-4$

=7

and $a_{3}-a_{2}=22-11$

=11

Since, $a_{2}-a_{1} \neq a_{3}-a_{2}$

Hence, it is not an AP.