A sequence of numbers begins with 12 and progresses geometrically. Each number is the previous number divided by 2.

Which value can be used as the common ratio in an explicit formula that represents the sequence?

2

6

12

In a geometric sequence, the common ratio (\(r\)) is the factor by which we multiply (or divide) each term to get the next term.

The sequence given starts at 12 and each subsequent number is obtained by dividing the previous number by 2. This means the common ratio is:

\[
r = \frac{12}{2} = \frac{1}{2}
\]

However, none of the options provided (2, 6, or 12) is \(\frac{1}{2}\), which would be the correct common ratio. Instead, the only way one of the options could fit into this scenario is if we think of 2, 6, or 12 as possible first terms or other elements, but not as the common ratio itself.

Do you need further clarification on geometric sequences?

---

Here are 5 related questions:
1. How is the common ratio of a geometric sequence determined?
2. What is the formula for the \(n\)-th term of a geometric sequence?
3. Can a geometric sequence have a negative common ratio?
4. How does changing the common ratio affect a geometric sequence?
5. How is the sum of an infinite geometric series calculated?

**Tip:** In geometric sequences, always identify the first term and the common ratio to construct the explicit formula.

A sequence of numbers begins with 12 and progresses geometrically. Each number is the previous number divided by 2. Which value can be used as the common ratio in an explicit formula that represents the sequence? 2, 6, or 12.

Explore how to determine the common ratio of a geometric sequence that starts at 12 and is divided by 2 in each step. Understand the explicit formula for the nth term and why the correct common ratio is 1/2, not one of the provided options (2, 6, or 12). Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation