The given number pattern is:
1, -3, 9, -27, ...

We can observe that the pattern alternates in signs, and the magnitude of each term is increasing exponentially. Let's break this down:

• The first term is 1.
• The second term is -3, which is 1 × -3.
• The third term is 9, which is -3 × -3.
• The fourth term is -27, which is 9 × -3.

This suggests that each term is being multiplied by -3 to get the next term. This is a geometric sequence where the common ratio $r = -3$.

Now, let's find the next few terms using this pattern:

• The fifth term is $-27 \times -3 = 81$.
• The sixth term is $81 \times -3 = -243$.
• The seventh term is $-243 \times -3 = 729$.

So, the complete sequence is: 1, -3, 9, -27, 81, -243, 729

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Would you like more details on geometric sequences or any other related concepts?

Related Questions:

1. What is the formula for the nth term of a geometric sequence?
2. How do you find the sum of the first n terms of a geometric sequence?
3. What happens if the common ratio of a geometric sequence is positive instead of negative?
4. How do you identify the type of sequence when given a list of numbers?
5. How can we apply geometric sequences in real-world problems?

Tip:

For geometric sequences, remember that each term is obtained by multiplying the previous term by a constant value, called the common ratio. This helps in easily predicting future terms!