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The given recurrence relation is:

\[
u_1 = 3, \quad u_n = 3 \times u_{n-1} - 4, \quad n \geq 2
\]

We will compute the first four terms \( u_1, u_2, u_3, u_4 \).

1. \( u_1 = 3 \) (given)
2. For \( u_2 \):
   \[
   u_2 = 3 \times u_1 - 4 = 3 \times 3 - 4 = 9 - 4 = 5
   \]
3. For \( u_3 \):
   \[
   u_3 = 3 \times u_2 - 4 = 3 \times 5 - 4 = 15 - 4 = 11
   \]
4. For \( u_4 \):
   \[
   u_4 = 3 \times u_3 - 4 = 3 \times 11 - 4 = 33 - 4 = 29
   \]

Thus, the first four terms are:

\[
u_1 = 3, \quad u_2 = 5, \quad u_3 = 11, \quad u_4 = 29
\]

Would you like more details or have any questions?

Here are 5 related questions you might consider:
1. What is the general form of the \(n\)-th term of this sequence?
2. Can we express this recurrence relation explicitly without recursion?
3. How does the growth rate of this sequence compare to a geometric sequence?
4. How would you modify the recurrence relation to generate a decreasing sequence?
5. What happens to the sequence as \(n\) approaches infinity?

**Tip:** Recurrence relations often reveal interesting long-term behavior, so analyzing them for limits or patterns can provide deeper insights.

Learn how to calculate the first 4 terms of a sequence given by the recurrence relation u_n = 3 * u_{n-1} - 4 with the initial condition u_1 = 3. This step-by-step solution is ideal for students in Grades 9-11.

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