Identify, complete, and describe number patterns in this math worksheet.

To solve the number pattern problems, we need to identify the rule governing each sequence and then use that rule to fill in the missing numbers. Let's go through each problem step by step.

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Problem 1:

Sequence: \( \boxed{53} \_\_ \_\_ \_\_ \_\_ 73 \_\_ 81 \_\_ \_\_ \)

#### Step 1: Identify the pattern
- The given numbers are: 53, 73, 81.
- The difference between 73 and 53 is \( 73 - 53 = 20 \).
- The difference between 81 and 73 is \( 81 - 73 = 8 \).

#### Step 2: Determine the rule
- The sequence alternates between adding 20 and adding 8.
- Starting from 53:
- Add 20: \( 53 + 20 = 73 \)
- Add 8: \( 73 + 8 = 81 \)

#### Step 3: Fill in the missing numbers
- From 53: \( 53 + 20 = 73 \) (already given)
- From 73: \( 73 + 8 = 81 \) (already given)
- Continue the pattern:
- Before 73: \( 73 - 20 = 53 \) (already given)
- Before 53: \( 53 - 8 = 45 \)
- After 81: \( 81 + 20 = 101 \)
- After 101: \( 101 + 8 = 109 \)

#### Final Sequence:
\[ 45, 53, 73, 81, 101, 109 \]

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Problem 2:

Sequence: \_\_ \_\_ 91 \_\_ 98 \_\_ 112 \_\_ \_\_ \_\_

#### Step 1: Identify the pattern
- The given numbers are: 91, 98, 112.
- The difference between 98 and 91 is \( 98 - 91 = 7 \).
- The difference between 112 and 98 is \( 112 - 98 = 14 \).

#### Step 2: Determine the rule
- The sequence alternates between adding 7 and adding 14.
- Starting from 91:
- Add 7: \( 91 + 7 = 98 \)
- Add 14: \( 98 + 14 = 112 \)

#### Step 3: Fill in the missing numbers
- Before 91: \( 91 - 7 = 84 \)
- Before 84: \( 84 - 14 = 70 \)
- After 98: \( 98 + 14 = 112 \) (already given)
- After 112: \( 112 + 7 = 119 \)
- After 119: \( 119 + 14 = 133 \)

#### Final Sequence:
\[ 70, 84, 91, 98, 112, 119, 133 \]

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Problem 3:

Sequence: \_\_ 11 \_\_ \_\_ \_\_ 26 \_\_ 29 \_\_

#### Step 1: Identify the pattern
- The given numbers are: 11, 26, 29.
- The difference between 26 and 11 is \( 26 - 11 = 15 \).
- The difference between 29 and 26 is \( 29 - 26 = 3 \).

#### Step 2: Determine the rule
- The sequence alternates between adding 15 and adding 3.
- Starting from 11:
- Add 15: \( 11 + 15 = 26 \)
- Add 3: \( 26 + 3 = 29 \)

#### Step 3: Fill in the missing numbers
- Before 11: \( 11 - 15 = -4 \)
- After 11: \( 11 + 3 = 14 \)
- After 14: \( 14 + 15 = 29 \) (already given)
- After 29: \( 29 + 3 = 32 \)

#### Final Sequence:
\[ -4, 11, 14, 26, 29, 32 \]

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Problem 4:

Sequence: \_\_ \_\_ \_\_ 242 \_\_ 342 \_\_ \_\_ 492 \_\_

#### Step 1: Identify the pattern
- The given numbers are: 242, 342, 492.
- The difference between 342 and 242 is \( 342 - 242 = 100 \).
- The difference between 492 and 342 is \( 492 - 342 = 150 \).

#### Step 2: Determine the rule
- The sequence alternates between adding 100 and adding 150.
- Starting from 242:
- Add 100: \( 242 + 100 = 342 \)
- Add 150: \( 342 + 150 = 492 \)

#### Step 3: Fill in the missing numbers
- Before 242: \( 242 - 150 = 92 \)
- Before 92: \( 92 - 100 = -8 \)
- After 342: \( 342 + 150 = 492 \) (already given)
- After 492: \( 492 + 100 = 592 \)

#### Final Sequence:
\[ -8, 92, 242, 342, 492, 592 \]

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Problem 5:

Sequence: \_\_ \_\_ 42 \_\_ 57 \_\_ 102 \_\_ \_\_

#### Step 1: Identify the pattern
- The given numbers are: 42, 57, 102.
- The difference between 57 and 42 is \( 57 - 42 = 15 \).
- The difference between 102 and 57 is \( 102 - 57 = 45 \).

#### Step 2: Determine the rule
- The sequence alternates between adding 15 and adding 45.
- Starting from 42:
- Add 15: \( 42 + 15 = 57 \)
- Add 45: \( 57 + 45 = 102 \)

#### Step 3: Fill in the missing numbers
- Before 42: \( 42 - 45 = -3 \)
- Before -3: \( -3 - 15 = -18 \)
- After 57: \( 57 + 45 = 102 \) (already given)
- After 102: \( 102 + 15 = 117 \)

#### Final Sequence:
\[ -18, -3, 42, 57, 102, 117 \]

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Problem 6:

Sequence: \_\_ 32 \_\_ \_\_ 52 \_\_ 62 \_\_ \_\_

#### Step 1: Identify the pattern
- The given numbers are: 32, 52, 62.
- The difference between 52 and 32 is \( 52 - 32 = 20 \).
- The difference between 62 and 52 is \( 62 - 52 = 10 \).

#### Step 2: Determine the rule
- The sequence alternates between adding 20 and adding 10.
- Starting from 32:
- Add 20: \( 32 + 20 = 52 \)
- Add 10: \( 52 + 10 = 62 \)

#### Step 3: Fill in the missing numbers
- Before 32: \( 32 - 10 = 22 \)
- After 32: \( 32 + 10 = 42 \)
- After 52: \( 52 + 10 = 62 \) (already given)
- After 62: \( 62 + 20 = 82 \)

#### Final Sequence:
\[ 22, 32, 42, 52, 62, 82 \]

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Problem 7:

Sequence: \_\_ \_\_ \_\_ 26 \_\_ \_\_ 30 \_\_ 32 \_\_

#### Step 1: Identify the pattern
- The given numbers are: 26, 30, 32.
- The difference between 30 and 26 is \( 30 - 26 = 4 \).
- The difference between 32 and 30 is \( 32 - 30 = 2 \).

#### Step 2: Determine the rule
- The sequence alternates between adding 4 and adding 2.
- Starting from 26:
- Add 4: \( 26 + 4 = 30 \)
- Add 2: \( 30 + 2 = 32 \)

#### Step 3: Fill in the missing numbers
- Before 26: \( 26 - 2 = 24 \)
- Before 24: \( 24 - 4 = 20 \)
- After 26: \( 26 + 2 = 28 \)
- After 30: \( 30 + 2 = 32 \) (already given)
- After 32: \( 32 + 4 = 36 \)

#### Final Sequence:
\[ 20, 24, 26, 28, 30, 32, 36 \]

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Problem 8:

Sequence: \_\_ \_\_ 62 \_\_ 64 \_\_ \_\_ 72 \_\_ \_\_

#### Step 1: Identify the pattern
- The given numbers are: 62, 64, 72.
- The difference between 64 and 62 is \( 64 - 62 = 2 \).
- The difference between 72 and 64 is \( 72 - 64 = 8 \).

#### Step 2: Determine the rule
- The sequence alternates between adding 2 and adding 8.
- Starting from 62:
- Add 2: \( 62 + 2 = 64 \)
- Add 8: \( 64 + 8 = 72 \)

#### Step 3: Fill in the missing numbers
- Before 62: \( 62 - 8 = 54 \)
- Before 54: \( 54 - 2 = 52 \)
- After 64: \( 64 + 8 = 72 \) (already given)
- After 72: \( 72 + 2 = 74 \)
- After 74: \( 74 + 8 = 82 \)

#### Final Sequence:
\[ 52, 54, 62, 64, 72, 74, 82 \]

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Problem 9:

Sequence: \_\_ \_\_ 79 \_\_ 106 \_\_ 124 \_\_ \_\_

#### Step 1: Identify the pattern
- The given numbers are: 79, 106, 124.
- The difference between 106 and 79 is \( 106 - 79 = 27 \).
- The difference between 124 and 106 is \( 124 - 106 = 18 \).

#### Step 2: Determine the rule
- The sequence alternates between adding 27 and adding 18.
- Starting from 79:
- Add 27: \( 79 + 27 = 106 \)
- Add 18: \( 106 + 18 = 124 \)

#### Step 3: Fill in the missing numbers
- Before 79: \( 79 - 18 = 61 \)
- Before 61: \( 61 - 27 = 34 \)
- After 106: \( 106 + 18 = 124 \) (already given)
- After 124: \( 124 + 27 = 151 \)

#### Final Sequence:
\[ 34, 61, 79, 106, 124, 151 \]

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Problem 10:

Sequence: \_\_ 96 \_\_ 126 \_\_ 136 \_\_ \_\_

#### Step 1: Identify the pattern
- The given numbers are: 96, 126, 136.
- The difference between 126 and 96 is \( 126 - 96 = 30 \).
- The difference between 136 and 126 is \( 136 - 126 = 10 \).

#### Step 2: Determine the rule
- The sequence alternates between adding 30 and adding 10.
- Starting from 96:
- Add 30: \( 96 + 30 = 126 \)
- Add 10: \( 126 + 10 = 136 \)

#### Step 3: Fill in the missing numbers
- Before 96: \( 96 - 10 = 86 \)
- After 96: \( 96 + 10 = 106 \)
- After 126: \( 126 + 10 = 136 \) (already given)
- After 136: \( 136 + 30 = 166 \)

#### Final Sequence:
\[ 86, 96, 106, 126, 136, 166 \]

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Final Answers:

1. \( \boxed{45, 53, 73, 81, 101, 109} \)
2. \( \boxed{70, 84, 91, 98, 112, 119, 133} \)
3. \( \boxed{-4, 11, 14, 26, 29, 32} \)
4. \( \boxed{-8, 92, 242, 342, 492, 592} \)
5. \( \boxed{-18, -3, 42, 57, 102, 117} \)
6. \( \boxed{22, 32, 42, 52, 62, 82} \)
7. \( \boxed{20, 24, 26, 28, 30, 32, 36} \)
8. \( \boxed{52, 54, 62, 64, 72, 74, 82} \)
9. \( \boxed{34, 61, 79, 106, 124, 151} \)
10. \( \boxed{86, 96, 106, 126, 136, 166} \)