Answer
Neither arithmetic, nor geometric
Work Step by Step
We are given the sequence:
$\{4n^2\}$
Compute the difference between two consecutive terms:
$a_{n+1}-a_n=4(n+1)^2-4n^2=4(n^2+2n+1)-4n^2=4n^2+8n+4-4n^2=8n+4$
As the difference between any consecutive terms is not constant, the sequence is not arithmetic.
Compute the ratio between two consecutive terms:
$\dfrac{a_{n+1}}{a_n}=\dfrac{4(n+1)^2}{4n^2}=\left(\dfrac{n+1}{n}\right)^2$
As the ratio between any consecutive terms is not constant, the sequence is not geometric.
So the sequence is neither arithmetic nor geometric.