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The given sequence is defined by the formula:

\[
a_n = -3 \cdot 4^{n-1}, \quad n = 1, 2, 3, \dots
\]

We are asked to find the first four terms of the sequence. Let's calculate them step by step.

1. For \( n = 1 \):
   \[
   a_1 = -3 \cdot 4^{1-1} = -3 \cdot 4^0 = -3 \cdot 1 = -3
   \]

2. For \( n = 2 \):
   \[
   a_2 = -3 \cdot 4^{2-1} = -3 \cdot 4^1 = -3 \cdot 4 = -12
   \]

3. For \( n = 3 \):
   \[
   a_3 = -3 \cdot 4^{3-1} = -3 \cdot 4^2 = -3 \cdot 16 = -48
   \]

4. For \( n = 4 \):
   \[
   a_4 = -3 \cdot 4^{4-1} = -3 \cdot 4^3 = -3 \cdot 64 = -192
   \]

So, the first four terms of the sequence are:

\[
a_1 = -3, \quad a_2 = -12, \quad a_3 = -48, \quad a_4 = -192
\]

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Do you want more details on any part of this solution or have any questions?

Here are 5 related questions for further exploration:
1. What is the general form of a geometric sequence?
2. How can we determine the common ratio in this sequence?
3. How would the sequence change if the base of the exponent were different?
4. What is the sum of the first four terms of this sequence?
5. How do we recognize if a sequence is increasing or decreasing?

**Tip:** In geometric sequences, each term is obtained by multiplying the previous one by a constant ratio, making them easy to compute step by step.

Hallar los primeros cuatro términos de la sucesión dado lo siguiente: a_n = -3 · 4^(n-1), n = 1, 2, 3...

Learn how to find the first four terms of the geometric sequence defined by a_n = -3 · 4^(n-1), suitable for Grades 8-10. This detailed solution covers key algebraic concepts such as sequences, exponential functions, and geometric sequences.

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