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.