find the common ratio in the following sequence -96,48,-24,-6,3

The given sequence is: \(-96, 48, -24, -6, 3\).

To find the common ratio \( r \) of a geometric sequence, we divide any term by the previous term. Let’s calculate:

\[
r = \frac{48}{-96} = -\frac{1}{2}
\]

Now, confirm the common ratio by dividing other consecutive terms:

\[
r = \frac{-24}{48} = -\frac{1}{2}
\]

\[
r = \frac{-6}{-24} = -\frac{1}{2}
\]

\[
r = \frac{3}{-6} = -\frac{1}{2}
\]

Since the ratio is consistent throughout the sequence, the common ratio \( r \) is \( -\frac{1}{2} \).

Would you like further details on this process or have any questions?

Here are some related questions you might want to explore:
1. What are the general formulas for a geometric sequence?
2. How do you determine if a sequence is arithmetic or geometric?
3. How can you find the sum of a geometric series?
4. What happens if the common ratio is greater than 1?
5. How does the sign of the common ratio affect the sequence?

**Tip:** Always verify the common ratio across multiple terms to ensure it's consistent throughout the sequence.

find the common ratio in the following sequence -96, 48, -24, -6, 3

Learn how to find the common ratio in the geometric sequence -96, 48, -24, -6, 3 with a step-by-step solution. This problem explores key mathematical concepts like geometric sequences and the formula for the common ratio. Suitable for students in Grades 8-10.

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