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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."

We define a sequence (u_n) by u_n = -3n + 7 for any natural number n. Determine the first 4 terms of the sequence.

Learn how to find the first four terms of an arithmetic sequence defined by u_n = -3n + 7. This solution covers arithmetic sequences and linear functions, suitable for students in Grades 6-8.

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