1. We are given the sequence $a_n = \frac{100n^3}{n^2 + 4}$ and asked to analyze or simplify it. 2. The formula for the sequence is already given: $a_n = \frac{100n^3}{n^2 + 4}$. 3. To understand the behavior of $a_n$, especially for large $n$, we can simplify the expression by dividing numerator and denominator by $n^2$: $$a_n = \frac{100n^3}{n^2 + 4} = \frac{100n^3 \div n^2}{(n^2 + 4) \div n^2} = \frac{100n}{1 + \frac{4}{n^2}}$$ 4. Using the cancellation notation: $$a_n = \frac{100\cancel{n^2}n}{\cancel{n^2} + 4} = \frac{100n}{1 + \frac{4}{n^2}}$$ 5. For very large $n$, $\frac{4}{n^2} \to 0$, so $a_n \approx 100n$. 6. This means the sequence grows approximately linearly with $n$ for large values. Final answer: $$a_n = \frac{100n^3}{n^2 + 4} = \frac{100n}{1 + \frac{4}{n^2}}$$ which behaves like $100n$ as $n$ becomes large.