Pattern Worksheets - Free Printable

Problem: Solve the number patterns and explain the solution.

#### 1) 5, 10, 20, 40, 80, _______

- Pattern Analysis:
- Each term is multiplied by 2 to get the next term.
- \( 5 \times 2 = 10 \)
- \( 10 \times 2 = 20 \)
- \( 20 \times 2 = 40 \)
- \( 40 \times 2 = 80 \)

- Next Term:
- \( 80 \times 2 = 160 \)

- Rule: Multiply each term by 2.

- Answer: \( 320 \)

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#### 2) 6, 12, 22, 44, 54, 108, _______

- Pattern Analysis:
- The pattern alternates between two rules:
1. Multiply by 2.
2. Add 10.
- \( 6 \times 2 = 12 \)
- \( 12 + 10 = 22 \)
- \( 22 \times 2 = 44 \)
- \( 44 + 10 = 54 \)
- \( 54 \times 2 = 108 \)

- Next Term:
- Following the alternating rule, after \( 108 \), we add 10.
- \( 108 + 10 = 118 \)

- Rule: Alternate between multiplying by 2 and adding 10.

- Answer: \( 118 \)

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#### 3) 17, 34, 35, 70, 71, 142, _______

- Pattern Analysis:
- The pattern alternates between two rules:
1. Multiply by 2.
2. Add 1.
- \( 17 \times 2 = 34 \)
- \( 34 + 1 = 35 \)
- \( 35 \times 2 = 70 \)
- \( 70 + 1 = 71 \)
- \( 71 \times 2 = 142 \)

- Next Term:
- Following the alternating rule, after \( 142 \), we add 1.
- \( 142 + 1 = 143 \)

- Rule: Alternate between multiplying by 2 and adding 1.

- Answer: \( 143 \)

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#### 4) 178, 172, 166, 160, 154, _______

- Pattern Analysis:
- Each term decreases by 6.
- \( 178 - 6 = 172 \)
- \( 172 - 6 = 166 \)
- \( 166 - 6 = 160 \)
- \( 160 - 6 = 154 \)

- Next Term:
- \( 154 - 6 = 148 \)

- Rule: Subtract 6 from each term.

- Answer: \( 148 \)

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#### 5) 15, 45, 135, 405, 1215, _______

- Pattern Analysis:
- Each term is multiplied by 3.
- \( 15 \times 3 = 45 \)
- \( 45 \times 3 = 135 \)
- \( 135 \times 3 = 405 \)
- \( 405 \times 3 = 1215 \)

- Next Term:
- \( 1215 \times 3 = 3645 \)

- Rule: Multiply each term by 3.

- Answer: \( 3645 \)

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Write your own pattern following this rule: x4, +2

- Rule: Multiply by 4, then add 2.
- Starting Number: Let's start with 1.
- Pattern:
- \( 1 \times 4 + 2 = 6 \)
- \( 6 \times 4 + 2 = 26 \)
- \( 26 \times 4 + 2 = 106 \)
- \( 106 \times 4 + 2 = 426 \)
- \( 426 \times 4 + 2 = 1706 \)

- Pattern: \( 1, 6, 26, 106, 426, 1706 \)

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Final Answers:

1. \( \boxed{320} \)
2. \( \boxed{118} \)
3. \( \boxed{143} \)
4. \( \boxed{148} \)
5. \( \boxed{3645} \)

Self-created Pattern:

\( \boxed{1, 6, 26, 106, 426, 1706} \)