The given expression for the $n$-th term of the sequence is $4n + 7$.

To find the first three terms of the sequence, we substitute values of $n$ into the expression for $n = 1, 2, 3$:

1. For $n = 1$: $4(1) + 7 = 4 + 7 = 11$

2. For $n = 2$: $4(2) + 7 = 8 + 7 = 15$

3. For $n = 3$: $4(3) + 7 = 12 + 7 = 19$

Therefore, the first three terms in the sequence are: $\boxed{11, 15, 19}$

Would you like a more detailed explanation or have any questions?

Here are some related questions for you:

1. How would you find the general expression for the $n$-th term of a sequence?
2. What is the common difference between consecutive terms in this sequence?
3. How can you find the 10th term in this sequence?
4. What happens if we change the expression to $2n + 5$?
5. How would you find the sum of the first five terms?

Tip: To find the term for any value of $n$, just substitute the value of $n$ into the general expression of the sequence.