how to get the ratio in geometric sequence

To find the ratio in a geometric sequence, follow these steps:

1. **Identify Two Consecutive Terms:** Select any two consecutive terms in the sequence. Let's call the first term \(a_n\) and the next term \(a_{n+1}\).

2. **Divide the Terms:** Divide the later term by the earlier term. The formula to find the common ratio \(r\) is:
   \[
   r = \frac{a_{n+1}}{a_n}
   \]
3. **Simplify the Fraction:** Simplify the result, if necessary, to get the common ratio \(r\).

**Example:**

Consider the geometric sequence: 2, 6, 18, 54,...

- Take two consecutive terms, say 6 and 2.
- Calculate the ratio:
  \[
  r = \frac{6}{2} = 3
  \]
- So, the common ratio \(r\) is 3.

Would you like more details, or do you have any questions?

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Here are 5 related questions:
1. How do you find the nth term in a geometric sequence?
2. What happens if the ratio in a geometric sequence is a fraction?
3. How can you determine if a sequence is geometric?
4. What is the sum of the first n terms of a geometric sequence?
5. How does the common ratio affect the behavior of a geometric sequence?

**Tip:** If the ratio is less than 1, the terms in the sequence will decrease over time, but if the ratio is greater than 1, the terms will increase.

Learn how to find the ratio in a geometric sequence with a step-by-step guide. Understand the formula to calculate the common ratio between consecutive terms. Includes an example with calculations for clarity. Suitable for high school students and anyone interested in mathematics.

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