To find the first three terms of the sequence, we need to evaluate the function $T(n) = 3n^2$ for $n = 1$, $n = 2$, and $n = 3$.

1. For $n = 1$: $T(1) = 3 \times 1^2 = 3 \times 1 = 3$

2. For $n = 2$: $T(2) = 3 \times 2^2 = 3 \times 4 = 12$

3. For $n = 3$: $T(3) = 3 \times 3^2 = 3 \times 9 = 27$

Answer:

The first three terms of the sequence are 3, 12, and 27.

Would you like further details or have any questions about this solution?

Here are five related questions to explore this concept further:

1. What is the fourth term of the sequence?
2. How can we determine if this sequence is arithmetic or geometric?
3. What is the general formula for the sum of the first $n$ terms of this sequence?
4. How would the sequence change if the formula were $T(n) = 3n^3$ instead?
5. How can you determine the common difference or ratio if it exists?

Tip: For polynomial sequences like this one, recognizing the degree of $n$ in the formula can help identify if it’s an arithmetic, geometric, or quadratic sequence.