Find the common ratio of the geometric sequence −15,−120,−960,...

The common ratio \( r \) of a geometric sequence is found by dividing any term by the previous term.

Given the sequence: \( -15, -120, -960, \dots \), let's calculate the ratio between the second and the first term, and the third and the second term to verify consistency:

1. \( r = \frac{-120}{-15} = 8 \)
2. \( r = \frac{-960}{-120} = 8 \)

Thus, the common ratio \( r \) is \( 8 \).

Would you like further details or have any questions about this?

Here are 5 related questions to deepen your understanding:
1. How do you derive the formula for the \( n \)-th term of a geometric sequence?
2. What happens to the sum of an infinite geometric series when the common ratio is between \(-1\) and \(1\)?
3. How does the sign of the common ratio affect the terms in a geometric sequence?
4. How can you tell whether a sequence is geometric just by looking at it?
5. What is the geometric mean, and how is it related to a geometric sequence?

**Tip:** In a geometric sequence, if the ratio between consecutive terms remains constant, it confirms that the sequence is geometric.

Find the common ratio of the geometric sequence −15, −120, −960,...

Learn how to find the common ratio of the geometric sequence −15, −120, −960 with a clear step-by-step solution. This problem introduces key algebraic concepts, including geometric sequences and the formula for calculating the common ratio. Suitable for students in Grades 8-10.

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