https://file.aiquickdraw.com/mathbot/file/17261971281556hxj73t4.jpg

In the image, it appears that you are working with sequences, both arithmetic and geometric. Let's go over the problems shown in the image:

### 2. Geometric Sequence
- **First term:** -9
- **Common ratio:** -2

This is a geometric sequence because each term is multiplied by a common ratio of -2 to get the next term. 
- The terms are: 
  \[
  -9, 18, -36, 72, -144, \dots
  \]
Each term is obtained by multiplying the previous term by -2.

### 3. Arithmetic Sequence
- **First term:** 0
- **Common difference:** -6

This is an arithmetic sequence because each term is found by subtracting 6 from the previous term.
- The terms are: 
  \[
  0, -6, -12, -18, -24, \dots
  \]
Each term is found by adding the common difference of -6 to the previous term.

### 4. Geometric Sequence
- **First term:** -3
- **Common ratio:** -\(\frac{1}{4}\)

This is another geometric sequence where each term is multiplied by -\(\frac{1}{4}\).
- The terms will be:
  \[
  -3, \frac{3}{4}, -\frac{3}{16}, \dots
  \]
Each term is obtained by multiplying the previous term by -\(\frac{1}{4}\).

---

Let me know if you'd like further explanations on any of these sequences or have any specific questions!

### 5 Questions for Exploration:
1. How do you derive the formula for the nth term in a geometric sequence?
2. What is the sum of the first n terms of an arithmetic sequence?
3. How can you determine if a sequence is geometric or arithmetic just by looking at a few terms?
4. How does the common ratio affect the behavior of a geometric sequence over time?
5. Can an arithmetic sequence ever have a common difference of 0? What would that mean?

### Tip:
When dealing with geometric sequences, if the common ratio's absolute value is less than 1, the terms will get smaller and smaller, eventually approaching zero.

The first term of the sequence is -9 and the common ratio is -2.

This problem focuses on identifying and solving arithmetic and geometric sequences. Learn how to find the nth term and determine common differences and ratios for these sequences, suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation