The given sequence is: \( 3, 9, 12, 26, 29, 51, 54 \).

Let's investigate the pattern.

### Step 1: Check for differences between consecutive terms:
\[
9 - 3 = 6
\]
\[
12 - 9 = 3
\]
\[
26 - 12 = 14
\]
\[
29 - 26 = 3
\]
\[
51 - 29 = 22
\]
\[
54 - 51 = 3
\]

So, the differences are: \( 6, 3, 14, 3, 22, 3 \).

It seems like there is an alternating pattern: first a larger difference, then 3, then another larger difference, then 3 again, and so on.

### Step 2: Analyze the pattern in the larger differences:
- \( 6 \)
- \( 14 \)
- \( 22 \)

These differences increase by 8 each time.

### Step 3: Predict the next term:
- The last difference was 3, so the next larger difference should be \( 22 + 8 = 30 \).

Thus, the next term in the sequence is:
\[
54 + 30 = 84
\]

### Conclusion:
The next term in the sequence is \( 84 \).

Would you like a detailed explanation, or do you have any questions?

Here are 5 related questions to expand on this topic:
1. What other sequences follow an alternating difference pattern?
2. Can you find a recursive formula for this sequence?
3. How can you identify arithmetic and geometric sequences from a set of numbers?
4. What is the general approach to finding the nth term of a sequence?
5. How do difference patterns help in finding missing terms?

**Tip**: Always check for alternating patterns or common difference steps when analyzing sequences!

Explore how to analyze a sequence with alternating differences using the example 3, 9, 12, 26, 29, 51, 54. Learn how to identify the pattern and predict the next term in the sequence (84) through detailed steps. Suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation