We are given a sequence $(u_n)$ defined by the formula:

$u_n = -3n + 7$ for all natural numbers $n$. We need to determine the first four terms of this sequence, namely $u_0$, $u_1$, $u_2$, and $u_3$.

Let's calculate each term:

1. For $u_0$: $u_0 = -3(0) + 7 = 0 + 7 = 7$

2. For $u_1$: $u_1 = -3(1) + 7 = -3 + 7 = 4$

3. For $u_2$: $u_2 = -3(2) + 7 = -6 + 7 = 1$

4. For $u_3$: $u_3 = -3(3) + 7 = -9 + 7 = -2$

So, the first four terms of the sequence are:

$u_0 = 7, \quad u_1 = 4, \quad u_2 = 1, \quad u_3 = -2$

Would you like further details or have any questions?

Here are five related questions to further explore:

1. How can we derive a general expression for the $n$-th term of an arithmetic sequence?
2. What is the common difference in the sequence $u_n = -3n + 7$?
3. How would the sequence change if the formula was $u_n = 3n + 7$?
4. Can you graph the first few terms of this sequence on a Cartesian plane?
5. How do you find the sum of the first $n$ terms of an arithmetic sequence?

Tip: In arithmetic sequences, the difference between consecutive terms is constant, and it is called the "common difference."