1. The problem is to analyze the sequence defined by $a_n = n^2 - 3$ and determine its properties. 2. The formula for the sequence is $a_n = n^2 - 3$, where $n$ is a positive integer. 3. To check if the sequence is arithmetic, we calculate the common difference $d = a_{n+1} - a_n$: $$d = ((n+1)^2 - 3) - (n^2 - 3) = (n^2 + 2n + 1 - 3) - (n^2 - 3) = 2n + 1$$ Since $d$ depends on $n$, the difference is not constant, so the sequence is not arithmetic. 4. To check if the sequence is geometric, we calculate the common ratio $r = \frac{a_{n+1}}{a_n}$: $$r = \frac{(n+1)^2 - 3}{n^2 - 3}$$ This ratio depends on $n$ and is not constant, so the sequence is not geometric. 5. Therefore, the sequence $a_n = n^2 - 3$ is neither arithmetic nor geometric. Final answer: The sequence is neither arithmetic nor geometric.