The sequence you've provided is: \(-2, 3, -4, 5, -6\).

This sequence alternates between negative and positive numbers, and it seems to involve increasing the absolute value by 1 each time. However, the pattern alternates in a specific way:

1. The first number is \(-2\), which is negative.
2. The next number is \(3\), which is positive.
3. The third number is \(-4\), which is negative again.
4. The fourth number is \(5\), which is positive.
5. The fifth number is \(-6\), which is negative.

**Pattern Explanation:**
- Odd positions have negative values: \(-2, -4, -6\)
- Even positions have positive values: \(3, 5\)

**Observations:**
- The absolute value of each term increases by 1 as you move from one term to the next.
- The sign alternates between negative and positive.

This sequence can be described by a formula for the \(n\)th term \(a_n\) as:

\[
a_n = (-1)^n \cdot (n + 1)
\]

**Where:**
- \( (-1)^n \) alternates the sign (negative for even \(n\) and positive for odd \(n\))
- \( n + 1 \) gives the absolute value of the term.

### Would you like to explore this pattern further or have any specific questions about it?

Here are five related questions:
1. What would be the 6th term in this sequence?
2. Can you generalize the formula for any alternating sequence like this?
3. How does the sequence change if the first term is positive?
4. What if the difference between consecutive terms is not 1 but some other constant?
5. How would the sequence behave if the signs didn't alternate?

**Tip:** When analyzing sequences, look for patterns in both the sign and magnitude of the terms. This helps in identifying the general formula.

Explore the pattern in the sequence -2, 3, -4, 5, -6, which involves alternating signs and increasing absolute values. Learn how to derive the general formula for the nth term and understand the underlying mathematical concepts. Ideal for students in Grades 9-12.

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