If I have a pattern of 7,9,14. 7,13,18, and 1,2,6 what can the net 3 number  be?

To determine the next three numbers in each pattern, let's analyze them individually.

### Pattern 1: \( 7, 9, 14 \)

- From \( 7 \) to \( 9 \), the difference is \( 9 - 7 = 2 \).
- From \( 9 \) to \( 14 \), the difference is \( 14 - 9 = 5 \).

The differences are \( +2 \) and \( +5 \). It appears that the differences are increasing by \( 3 \). So, the next difference should be \( 5 + 3 = 8 \).

- The next number would be \( 14 + 8 = 22 \).

For the following number, the difference should increase by another \( 3 \), i.e., \( 8 + 3 = 11 \).

- The next number would be \( 22 + 11 = 33 \).

The next difference will be \( 11 + 3 = 14 \).

- The next number would be \( 33 + 14 = 47 \).

So, the next three numbers in the first pattern are: **22, 33, 47**.

### Pattern 2: \( 7, 13, 18 \)

- From \( 7 \) to \( 13 \), the difference is \( 13 - 7 = 6 \).
- From \( 13 \) to \( 18 \), the difference is \( 18 - 13 = 5 \).

The differences are decreasing by \( 1 \), from \( +6 \) to \( +5 \). If the differences continue decreasing by \( 1 \), the next difference should be \( 5 - 1 = 4 \).

- The next number would be \( 18 + 4 = 22 \).

The next difference should be \( 4 - 1 = 3 \).

- The next number would be \( 22 + 3 = 25 \).

The next difference should be \( 3 - 1 = 2 \).

- The next number would be \( 25 + 2 = 27 \).

So, the next three numbers in the second pattern are: **22, 25, 27**.

### Pattern 3: \( 1, 2, 6 \)

- From \( 1 \) to \( 2 \), the difference is \( 2 - 1 = 1 \).
- From \( 2 \) to \( 6 \), the difference is \( 6 - 2 = 4 \).

The differences are \( +1 \) and \( +4 \). The differences increased by \( 3 \). If the difference continues increasing by \( 3 \), the next difference should be \( 4 + 3 = 7 \).

- The next number would be \( 6 + 7 = 13 \).

The next difference should increase by \( 3 \), so it becomes \( 7 + 3 = 10 \).

- The next number would be \( 13 + 10 = 23 \).

The next difference should increase by \( 3 \), so it becomes \( 10 + 3 = 13 \).

- The next number would be \( 23 + 13 = 36 \).

So, the next three numbers in the third pattern are: **13, 23, 36**.

### Summary of the next three numbers in each pattern:
- First pattern: **22, 33, 47**
- Second pattern: **22, 25, 27**
- Third pattern: **13, 23, 36**

Would you like more details on any of these patterns or have further questions?

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Here are 5 related questions:
1. How can we identify the general rule for an arithmetic sequence?
2. What is the difference between arithmetic and geometric sequences?
3. Can differences in a pattern always be constant, or can they follow a formula?
4. What are the characteristics of a quadratic number sequence?
5. How can you find the \(n\)-th term of a pattern if given a few terms?

**Tip**: If the differences in a sequence aren't constant, check if they are increasing or decreasing by a set number. This might indicate a second-level pattern.

If I have a pattern of 7,9,14. 7,13,18, and 1,2,6 what can the next 3 numbers be?

Discover how to find the next three numbers in patterns such as 7, 9, 14; 7, 13, 18; and 1, 2, 6. This math problem involves understanding arithmetic sequences and difference patterns, making it suitable for students in Grades 5-8. Learn how to calculate the differences and identify the rules governing each sequence.

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