What geometric sequence has the series of 136?

L. 1, 5, 25, 105
M. 6, 18, 108
N. 1, 7, 14, 28, 56
O. None of the above

To identify which geometric sequence has a series sum of 136, we need to determine if the sum of terms in any of the given sequences equals 136. Here's the breakdown:

### Sequence L: \( 1, 5, 25, 105 \)
- The ratio between consecutive terms is not constant. \( \frac{5}{1} = 5 \), but \( \frac{25}{5} = 5 \), and \( \frac{105}{25} \neq 5 \), so it's not geometric.

### Sequence M: \( 6, 18, 108 \)
- Common ratio \( \frac{18}{6} = 3 \) and \( \frac{108}{18} = 6 \), so the ratio isn't constant. Therefore, this is not a geometric sequence either.

### Sequence N: \( 1, 7, 14, 28, 56 \)
- Common ratio \( \frac{7}{1} = 7 \), but \( \frac{14}{7} = 2 \). The ratio changes, so it is not geometric.

### Conclusion:
Since none of the provided sequences are geometric, **option O** ("None of the above") is correct.

Would you like more details on geometric sequences or have any questions?

Here are 5 related questions:
1. What defines a geometric sequence?
2. How do you find the sum of a geometric series?
3. Can a sequence have different ratios and still be geometric?
4. What are examples of geometric sequences in nature?
5. How do arithmetic and geometric sequences differ?

**Tip:** Always check if the ratio between consecutive terms is constant to confirm if a sequence is geometric.

What geometric sequence has the series of 136?
L. 1, 5, 25, 105
M. 6, 18, 108
N. 1, 7, 14, 28, 56
O. None of the above

Explore how to identify which sequence, if any, is a geometric sequence with a series sum of 136. The problem involves understanding geometric sequences, checking for a common ratio, and applying the sum formula. Ideal for students in Grades 8-10.

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