The question asks us to identify which sequence is a "geometric progression" (dãy số nhân). A geometric progression is a sequence where each term is obtained by multiplying the previous term by a fixed constant (the common ratio).

Let's analyze the options:

A. 1, 2, 4, 6

• Ratios: $\frac{2}{1} = 2$, $\frac{4}{2} = 2$, $\frac{6}{4} = 1.5$
• The ratios are not constant. This is not a geometric progression.

B. 1, 3, 12, 60

• Ratios: $\frac{3}{1} = 3$, $\frac{12}{3} = 4$, $\frac{60}{12} = 5$
• The ratios are not constant. This is not a geometric progression.

C. −1, 4, −16, 64

• Ratios: $\frac{4}{-1} = -4$, $\frac{-16}{4} = -4$, $\frac{64}{-16} = -4$
• The ratios are constant ($-4$). This is a geometric progression.

D. −1, −5, −25, 125

• Ratios: $\frac{-5}{-1} = 5$, $\frac{-25}{-5} = 5$, $\frac{125}{-25} = -5$
• The ratios are not constant. This is not a geometric progression.

Answer: C. −1, 4, −16, 64

Would you like further explanation or more examples of geometric progressions?

5 Related Questions:

1. What are the differences between arithmetic and geometric progressions?
2. How do you find the $n$-th term of a geometric progression?
3. Can a geometric progression include negative numbers?
4. How can we calculate the sum of a geometric series?
5. What are real-world applications of geometric progressions?

Tip:

To quickly identify a geometric progression, check if the ratio between consecutive terms remains constant throughout the sequence!