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Question 8 of 15 ›
Identify a pattern in the given list of numbers. Then use this pattern to find the next number. (More than one patter might exist, so it is possible that there is more than one correct answar.)
1, 4, 1, 12, 1, 36, 1,
This test: 15 points) possible
This question: 1 points) possible
The next number is

Let's analyze the pattern in the given sequence:  
\[ 1, 4, 1, 12, 1, 36, 1, \dots \]

### Observations:
- Every second number (the even positions) increases in a certain way:  
  - 4, 12, 36, ...

### Pattern in the even-positioned numbers:
- From 4 to 12, the factor is 3 (since \( 4 \times 3 = 12 \)).
- From 12 to 36, the factor is also 3 (since \( 12 \times 3 = 36 \)).

Thus, the numbers in even positions follow a pattern where each number is multiplied by 3.

### Predicting the next number:
- The next number in an even position (after 36) should be \( 36 \times 3 = 108 \).

Therefore, the next number in the sequence is **108**.

### Final sequence:
\[ 1, 4, 1, 12, 1, 36, 1, 108 \]

Would you like more details or have any questions?  

Here are five related questions to deepen understanding:
1. What if the sequence only alternated between 1 and powers of 4?
2. How would the sequence change if the multiplier were 2 instead of 3?
3. Can you derive a formula for the even-position numbers?
4. How would the pattern continue if the odd-positioned numbers also followed a rule?
5. Could this sequence represent a geometric progression in some way?

**Tip:** Identifying patterns often requires examining different segments separately, such as odd and even positions, to uncover hidden relationships.

Identify a pattern in the given list of numbers. Then use this pattern to find the next number. (More than one pattern might exist, so it is possible that there is more than one correct answer.) 1, 4, 1, 12, 1, 36, 1, ... The next number is?

Discover how to identify patterns in the sequence 1, 4, 1, 12, 1, 36, 1 and find the next number. This step-by-step explanation covers the concept of multiplying the even-positioned numbers by 3 and highlights key mathematical ideas in pattern recognition. Suitable for Grades 5-7.

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