1. The problem states that the $n^{th}$ term of a sequence is given by the formula $a_n = 4n^2$. 2. We need to find the first three terms of the sequence, which means we will calculate $a_1$, $a_2$, and $a_3$. 3. Using the formula $a_n = 4n^2$, substitute $n=1$: $$a_1 = 4 \times 1^2 = 4 \times 1 = 4$$ 4. Substitute $n=2$: $$a_2 = 4 \times 2^2 = 4 \times 4 = 16$$ 5. Substitute $n=3$: $$a_3 = 4 \times 3^2 = 4 \times 9 = 36$$ 6. Therefore, the first three terms of the sequence are $4$, $16$, and $36$.