Patterns Worksheets | Dynamically Created Patterns Worksheets - Free Printable

I'll work through each numerical series step by step to find the patterns and complete them.

Series 1: 4, 8, 10, 20, 22, 44, 46, __, __, __
- 4 × 2 = 8
- 8 + 2 = 10
- 10 × 2 = 20
- 20 + 2 = 22
- 22 × 2 = 44
- 44 + 2 = 46
- Pattern: multiply by 2, then add 2 (alternating)
- 46 × 2 = 92
- 92 + 2 = 94
- 94 × 2 = 188
Answer: 92, 94, 188

Series 2: 1, 3, -1, -3, -7, -21, -25, __, __, __
- 1 + 2 = 3
- 3 - 4 = -1
- -1 - 2 = -3
- -3 - 4 = -7
- -7 × 3 = -21
- -21 - 4 = -25
Let me reconsider...
- 1 × 3 = 3
- 3 - 4 = -1
- -1 × 3 = -3
- -3 - 4 = -7
- -7 × 3 = -21
- -21 - 4 = -25
Pattern: multiply by 3, then subtract 4 (alternating)
- -25 × 3 = -75
- -75 - 4 = -79
- -79 × 3 = -237
Answer: -75, -79, -237

Series 3: 0, 1, 1, 2, 3, 5, 8, __, __, __
This is the Fibonacci sequence where each number is the sum of the two previous numbers.
- 0 + 1 = 1
- 1 + 1 = 2
- 1 + 2 = 3
- 2 + 3 = 5
- 3 + 5 = 8
- 5 + 8 = 13
- 8 + 13 = 21
- 13 + 21 = 34
Answer: 13, 21, 34

Series 4: 4, 12, 16, 48, 52, 156, 160, __, __, __
- 4 × 3 = 12
- 12 + 4 = 16
- 16 × 3 = 48
- 48 + 4 = 52
- 52 × 3 = 156
- 156 + 4 = 160
Pattern: multiply by 3, then add 4 (alternating)
- 160 × 3 = 480
- 480 + 4 = 484
- 484 × 3 = 1452
Answer: 480, 484, 1452

Series 5: 9, 12, 7, 10, 5, 8, 3, __, __, __
- 9 + 3 = 12
- 12 - 5 = 7
- 7 + 3 = 10
- 10 - 5 = 5
- 5 + 3 = 8
- 8 - 5 = 3
Pattern: add 3, then subtract 5 (alternating)
- 3 + 3 = 6
- 6 - 5 = 1
- 1 + 3 = 4
Answer: 6, 1, 4

Series 6: 16, 22, 19, 25, 22, 28, 25, __, __, __
- 16 + 6 = 22
- 22 - 3 = 19
- 19 + 6 = 25
- 25 - 3 = 22
- 22 + 6 = 28
- 28 - 3 = 25
Pattern: add 6, then subtract 3 (alternating)
- 25 + 6 = 31
- 31 - 3 = 28
- 28 + 6 = 34
Answer: 31, 28, 34

Series 7: 4, 12, 16, 48, 52, 156, 160, __, __, __
Same as Series 4:
- 4 × 3 = 12
- 12 + 4 = 16
- 16 × 3 = 48
- 48 + 4 = 52
- 52 × 3 = 156
- 156 + 4 = 160
Pattern: multiply by 3, then add 4 (alternating)
- 160 × 3 = 480
- 480 + 4 = 484
- 484 × 3 = 1452
Answer: 480, 484, 1452

Series 8: 4, 8, 1, 2, -5, -10, -17, __, __, __
- 4 × 2 = 8
- 8 - 7 = 1
- 1 × 2 = 2
- 2 - 7 = -5
- -5 × 2 = -10
- -10 - 7 = -17
Pattern: multiply by 2, then subtract 7 (alternating)
- -17 × 2 = -34
- -34 - 7 = -41
- -41 × 2 = -82
Answer: -34, -41, -82

Series 9: 22, 28, 21, 27, 20, 26, 19, __, __, __
- 22 + 6 = 28
- 28 - 7 = 21
- 21 + 6 = 27
- 27 - 7 = 20
- 20 + 6 = 26
- 26 - 7 = 19
Pattern: add 6, then subtract 7 (alternating)
- 19 + 6 = 25
- 25 - 7 = 18
- 18 + 6 = 24
Answer: 25, 18, 24

Series 10: 1, 2, -4, -8, -14, -28, -34, __, __, __
- 1 × 2 = 2
- 2 - 6 = -4
- -4 × 2 = -8
- -8 - 6 = -14
- -14 × 2 = -28
- -28 - 6 = -34
Pattern: multiply by 2, then subtract 6 (alternating)
- -34 × 2 = -68
- -68 - 6 = -74
- -74 × 2 = -148
Answer: -68, -74, -148

Final Answer:
1) 92, 94, 188
2) -75, -79, -237
3) 13, 21, 34
4) 480, 484, 1452
5) 6, 1, 4
6) 31, 28, 34
7) 480, 484, 1452
8) -34, -41, -82
9) 25, 18, 24
10) -68, -74, -148