To identify which of the sequences in the image is geometric, we need to check if there is a consistent ratio between consecutive terms.

Let's analyze each sequence:

1. {3, 6, 24, 36, ...}

   • Ratio between the first two terms: $\frac{6}{3} = 2$
   • Ratio between the second and third terms: $\frac{24}{6} = 4$
   • Since the ratios are not consistent, this is not a geometric sequence.

2. {10, 50, 250, 1250, ...}

   • Ratio between the first two terms: $\frac{50}{10} = 5$
   • Ratio between the second and third terms: $\frac{250}{50} = 5$
   • Ratio between the third and fourth terms: $\frac{1250}{250} = 5$
   • Since the ratios are consistent, this is a geometric sequence.

3. {14, 19, 24, 29, ...}

   • Difference between terms: $19 - 14 = 5$, $24 - 19 = 5$, $29 - 24 = 5$
   • This is an arithmetic sequence, not geometric.

4. {50, 40, 30, 20, ...}

   • Difference between terms: $40 - 50 = -10$, $30 - 40 = -10$, $20 - 30 = -10$
   • This is also an arithmetic sequence, not geometric.

Conclusion:

The second sequence {10, 50, 250, 1250, ...} is the geometric sequence.

Would you like further clarification or details on geometric sequences?

1. How do you find the common ratio in a geometric sequence?
2. What is the general form of a geometric sequence?
3. Can a geometric sequence have a common ratio of 1?
4. How do arithmetic and geometric sequences differ in their behavior?
5. How would you find the nth term of a geometric sequence?

Tip: In a geometric sequence, multiplying the previous term by the common ratio gives you the next term.