https://file.aiquickdraw.com/mathbot/file/1726031562706hlvfmy5b.jpg

The sequence provided in the image is:  
\[ -2, 4, -8, 16, -32 \]

This is a geometric sequence because each term is obtained by multiplying the previous term by a constant ratio. Let's find the common ratio \( r \).

\[
r = \frac{4}{-2} = -2
\]
\[
r = \frac{-8}{4} = -2
\]
\[
r = \frac{16}{-8} = -2
\]

So, the common ratio \( r \) is \(-2\).

The general formula for the \(n\)-th term of a geometric sequence is:
\[
a_n = a_1 \cdot r^{n-1}
\]
Where:
- \( a_1 \) is the first term of the sequence.
- \( r \) is the common ratio.
- \( n \) is the term number.

Here, \( a_1 = -2 \) and \( r = -2 \). Therefore, the formula for the \(n\)-th term becomes:
\[
a_n = -2 \cdot (-2)^{n-1}
\]
Thus, the \(n\)-th term of the sequence is:
\[
a_n = -2 \cdot (-2)^{n-1}
\]

Would you like more details on this solution or have any other questions?

### Related Questions:
1. How do you determine whether a sequence is arithmetic or geometric?
2. What happens if the common ratio in a geometric sequence is a fraction?
3. Can a sequence have both positive and negative terms and still be geometric?
4. How would the formula change if the first term were positive instead of negative?
5. What is the sum of the first \(n\) terms of a geometric sequence?

### Tip:
In geometric sequences, the sign of the common ratio determines whether the sequence alternates between positive and negative values.

Find the nth term of the sequence: -2, 4, -8, 16, -32

Learn how to find the nth term of the geometric sequence -2, 4, -8, 16, -32 using the general formula for geometric sequences. This problem covers key concepts such as the common ratio and the formula for the nth term. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation