Determine if the sequence below is arithmetic or geometric and determine the common difference / ratio in simplest form.

4, comma, 24, comma, 144, comma, point, point, .

4,24,144,

The given sequence is:

\[
4, 24, 144, \dots
\]

### Step 1: Check for an arithmetic sequence
An arithmetic sequence has a common difference between consecutive terms. Let's check:

- The difference between the second and first term: \( 24 - 4 = 20 \)
- The difference between the third and second term: \( 144 - 24 = 120 \)

Since the differences are not the same, the sequence is **not arithmetic**.

### Step 2: Check for a geometric sequence
A geometric sequence has a common ratio between consecutive terms. Let's check:

- The ratio between the second and first term: \( \frac{24}{4} = 6 \)
- The ratio between the third and second term: \( \frac{144}{24} = 6 \)

Since the ratios are the same, the sequence is **geometric** with a common ratio of \( r = 6 \).

### Conclusion:
The sequence is geometric with a common ratio of \( r = 6 \).

Would you like further details or clarifications?

Here are 5 related questions to explore:
1. What is the next term in the sequence?
2. How would the sum of the first 5 terms of this geometric sequence be calculated?
3. What are the key differences between arithmetic and geometric sequences?
4. Can a sequence be both arithmetic and geometric?
5. How does the geometric mean relate to geometric sequences?

**Tip:** In a geometric sequence, each term is found by multiplying the previous term by the common ratio.

Determine if the sequence below is arithmetic or geometric and determine the common difference / ratio in simplest form. 4, 24, 144, ...

Learn how to determine if the sequence 4, 24, 144, ... is arithmetic or geometric with a step-by-step solution. This problem covers key concepts such as arithmetic and geometric sequences, common differences, and common ratios. Suitable for students in Grades 7-9.

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