known number sequence 8748, 2916, a, 324, b, 36, 12 what is the replacement for a and b

To find the replacement for \(a\) and \(b\) in the sequence \(8748, 2916, a, 324, b, 36, 12\), we need to identify the pattern in the sequence.

Let's examine the relationship between consecutive terms:

1. \(8748\) to \(2916\):
   \[
   \frac{8748}{2916} = 3
   \]
   So, \(2916 = \frac{8748}{3}\).

2. \(2916\) to \(a\):
   \[
   a = \frac{2916}{3} = 972
   \]

3. \(a\) to \(324\):
   \[
   \frac{972}{324} = 3
   \]
   So, \(324 = \frac{972}{3}\).

4. \(324\) to \(b\):
   \[
   b = \frac{324}{3} = 108
   \]

5. \(b\) to \(36\):
   \[
   \frac{108}{36} = 3
   \]
   So, \(36 = \frac{108}{3}\).

6. \(36\) to \(12\):
   \[
   \frac{36}{12} = 3
   \]
   So, \(12 = \frac{36}{3}\).

Based on this pattern, every term is \(\frac{1}{3}\) of the previous term. Thus, the sequence with the replacements for \(a\) and \(b\) is:

\[
8748, 2916, 972, 324, 108, 36, 12
\]

So, the values for \(a\) and \(b\) are:

- \(a = 972\)
- \(b = 108\)

Would you like more details or have any questions? 

Here are 8 related questions to consider:

1. How can the general formula for this sequence be written?
2. What are other types of common mathematical sequences?
3. How does identifying patterns in sequences help in solving real-world problems?
4. What is the importance of recognizing geometric sequences in algebra?
5. Can you provide an example of an arithmetic sequence?
6. How do you find the \(n\)-th term of a geometric sequence?
7. What are some practical applications of geometric sequences?
8. How do sequences relate to series in mathematics?

**Tip:** When working with sequences, look for common ratios or differences to identify whether they are geometric or arithmetic sequences.

Learn how to identify patterns in mathematical sequences with a detailed example. This problem explores the concept of geometric sequences and how to find missing terms in a sequence. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation