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.