Patterns Worksheets | Dynamically Created Patterns Worksheets - Free Printable

To solve the problem of completing the number series, we need to identify the pattern in each sequence. Let's analyze each row step by step.

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Row 1:

Sequence: \( 5, 6, \_, \_, 9, \_, \_, \_ \)

- The difference between the first two numbers is \( 6 - 5 = 1 \).
- Assuming the pattern is an increment of 1, the next numbers would be:
- \( 6 + 1 = 7 \)
- \( 7 + 1 = 8 \)
- \( 9 + 1 = 10 \)
- \( 10 + 1 = 11 \)
- \( 11 + 1 = 12 \)

So, the completed sequence is:
\[ 5, 6, 7, 8, 9, 10, 11, 12 \]

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Row 2:

Sequence: \( \_, 11, \_, \_, \_, 15, \_, 17 \)

- The last two numbers are \( 15 \) and \( 17 \), with a difference of \( 17 - 15 = 2 \).
- Assuming the pattern is an increment of 2, we can work backward and forward:
- Before 11: \( 11 - 2 = 9 \)
- After 11: \( 11 + 2 = 13 \)
- After 13: \( 13 + 2 = 15 \) (already given)
- After 15: \( 15 + 2 = 17 \) (already given)
- Before 9: \( 9 - 2 = 7 \)

So, the completed sequence is:
\[ 7, 9, 11, 13, 15, 17 \]

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Row 3:

Sequence: \( 7, \_, \_, \_, 11, \_, 13, \_ \)

- The difference between 11 and 13 is \( 13 - 11 = 2 \).
- Assuming the pattern is an increment of 2, we can fill in the missing numbers:
- Before 11: \( 11 - 2 = 9 \)
- Before 9: \( 9 - 2 = 7 \) (already given)
- Before 7: \( 7 - 2 = 5 \)
- After 11: \( 11 + 2 = 13 \) (already given)
- After 13: \( 13 + 2 = 15 \)

So, the completed sequence is:
\[ 5, 7, 9, 11, 13, 15 \]

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Row 4:

Sequence: \( \_, 5, \_, \_, \_, 9, \_, 11 \)

- The difference between 5 and 9 is \( 9 - 5 = 4 \), which suggests an increment of 2.
- Assuming the pattern is an increment of 2, we can fill in the missing numbers:
- Before 5: \( 5 - 2 = 3 \)
- After 5: \( 5 + 2 = 7 \)
- After 7: \( 7 + 2 = 9 \) (already given)
- After 9: \( 9 + 2 = 11 \) (already given)
- Before 3: \( 3 - 2 = 1 \)

So, the completed sequence is:
\[ 1, 3, 5, 7, 9, 11 \]

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Row 5:

Sequence: \( \_, \_, 3, \_, 5, 6, \_, \_ \)

- The difference between 5 and 6 is \( 6 - 5 = 1 \).
- Assuming the pattern is an increment of 1, we can fill in the missing numbers:
- Before 3: \( 3 - 1 = 2 \)
- Before 2: \( 2 - 1 = 1 \)
- After 3: \( 3 + 1 = 4 \) (already given as 5, so this part might have a different pattern)
- After 6: \( 6 + 1 = 7 \)
- After 7: \( 7 + 1 = 8 \)

So, the completed sequence is:
\[ 1, 2, 3, 4, 5, 6, 7, 8 \]

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Row 6:

Sequence: \( 13, \_, \_, \_, 17, 18, \_, \_ \)

- The difference between 17 and 18 is \( 18 - 17 = 1 \).
- Assuming the pattern is an increment of 1, we can fill in the missing numbers:
- Before 17: \( 17 - 1 = 16 \)
- Before 16: \( 16 - 1 = 15 \)
- Before 15: \( 15 - 1 = 14 \)
- After 18: \( 18 + 1 = 19 \)
- After 19: \( 19 + 1 = 20 \)

So, the completed sequence is:
\[ 13, 14, 15, 16, 17, 18, 19, 20 \]

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Row 7:

Sequence: \( \_, 12, 13, \_, 15, \_, \_, \_ \)

- The difference between 12 and 13 is \( 13 - 12 = 1 \).
- Assuming the pattern is an increment of 1, we can fill in the missing numbers:
- Before 12: \( 12 - 1 = 11 \)
- After 13: \( 13 + 1 = 14 \)
- After 14: \( 14 + 1 = 15 \) (already given)
- After 15: \( 15 + 1 = 16 \)
- After 16: \( 16 + 1 = 17 \)
- After 17: \( 17 + 1 = 18 \)

So, the completed sequence is:
\[ 11, 12, 13, 14, 15, 16, 17, 18 \]

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Row 8:

Sequence: \( \_, 1, \_, \_, \_, 6, 7 \)

- The difference between 6 and 7 is \( 7 - 6 = 1 \).
- Assuming the pattern is an increment of 1, we can fill in the missing numbers:
- Before 1: \( 1 - 1 = 0 \)
- After 1: \( 1 + 1 = 2 \)
- After 2: \( 2 + 1 = 3 \)
- After 3: \( 3 + 1 = 4 \)
- After 4: \( 4 + 1 = 5 \)
- After 5: \( 5 + 1 = 6 \) (already given)
- After 6: \( 6 + 1 = 7 \) (already given)

So, the completed sequence is:
\[ 0, 1, 2, 3, 4, 5, 6, 7 \]

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Row 9:

Sequence: \( 9, \_, \_, \_, 13, \_, \_, 16 \)

- The difference between 13 and 16 is \( 16 - 13 = 3 \), which suggests an increment of 1.
- Assuming the pattern is an increment of 1, we can fill in the missing numbers:
- Before 13: \( 13 - 1 = 12 \)
- Before 12: \( 12 - 1 = 11 \)
- Before 11: \( 11 - 1 = 10 \)
- After 13: \( 13 + 1 = 14 \)
- After 14: \( 14 + 1 = 15 \)
- After 15: \( 15 + 1 = 16 \) (already given)

So, the completed sequence is:
\[ 9, 10, 11, 12, 13, 14, 15, 16 \]

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Row 10:

Sequence: \( 12, 13, \_, \_, \_, 17, \_, \_ \)

- The difference between 13 and 17 is \( 17 - 13 = 4 \), which suggests an increment of 1.
- Assuming the pattern is an increment of 1, we can fill in the missing numbers:
- After 13: \( 13 + 1 = 14 \)
- After 14: \( 14 + 1 = 15 \)
- After 15: \( 15 + 1 = 16 \)
- After 17: \( 17 + 1 = 18 \)
- After 18: \( 18 + 1 = 19 \)

So, the completed sequence is:
\[ 12, 13, 14, 15, 16, 17, 18, 19 \]

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Final Answer:

\[
\boxed{
\begin{array}{llllllll}
5, & 6, & 7, & 8, & 9, & 10, & 11, & 12 \\
7, & 9, & 11, & 13, & 15, & 17 \\
5, & 7, & 9, & 11, & 13, & 15 \\
1, & 3, & 5, & 7, & 9, & 11 \\
1, & 2, & 3, & 4, & 5, & 6, & 7, & 8 \\
13, & 14, & 15, & 16, & 17, & 18, & 19, & 20 \\
11, & 12, & 13, & 14, & 15, & 16, & 17, & 18 \\
0, & 1, & 2, & 3, & 4, & 5, & 6, & 7 \\
9, & 10, & 11, & 12, & 13, & 14, & 15, & 16 \\
12, & 13, & 14, & 15, & 16, & 17, & 18, & 19 \\
\end{array}
}
\]