Patterns Worksheets | Dynamically Created Patterns Worksheets - Free Printable

I'll solve each numerical series step by step, looking for patterns.

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

Series 2: 1, 3, -1, -3, -7, -21, -25, __, __, __
Let me check the pattern more carefully:
- 1 to 3: +2
- 3 to -1: -4
- -1 to -3: -2
- -3 to -7: -4
- -7 to -21: -14 (or ×3)
- -21 to -25: -4

This seems inconsistent. Let me try another approach:
Looking at pairs or alternating patterns...
Actually, let me reconsider: 1, 3, -1, -3, -7, -21, -25
Maybe it's two interleaved sequences?
Odd positions: 1, -1, -7, -25 → differences: -2, -6, -18 (multiplying by 3?)
Even positions: 3, -3, -21 → differences: -6, -18 (also multiplying by 3?)

If this pattern continues:
Next odd position: -25 - 54 = -79 (difference of -54, which is -18×3)
Next even position: -21 - 54 = -75
Next odd position: -79 - 162 = -241

Wait, let me reconsider the whole sequence differently.

Series 3: 0, 1, 1, 2, 3, 5, 8, __, __, __
This is the Fibonacci sequence! Each number is the sum of the previous two.
- 0 + 1 = 1
- 1 + 1 = 2
- 1 + 2 = 3
- 2 + 3 = 5
- 3 + 5 = 8
- 5 + 8 = 13
- 8 + 13 = 21
- 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

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: +3, -5 (alternating)
- 3 + 3 = 6
- 6 - 5 = 1
- 1 + 3 = 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: +6, -3 (alternating)
- 25 + 6 = 31
- 31 - 3 = 28
- 28 + 6 = 34

Series 7: 4, 12, 16, 48, 52, 156, 160, __, __, __
This is identical to Series 4.
- 160 × 3 = 480
- 480 + 4 = 484
- 484 × 3 = 1452

Series 8: 4, 8, 1, 2, -5, -10, -17, __, __, __
Let me look at this carefully:
- 4 to 8: +4
- 8 to 1: -7
- 1 to 2: +1
- 2 to -5: -7
- -5 to -10: -5
- -10 to -17: -7

Hmm, not obvious. Let me try pairs:
(4, 8), (1, 2), (-5, -10), (-17, ?)
Within pairs: 4×2=8, 1×2=2, -5×2=-10, so -17×2=-34

Between pairs: 8 to 1: -7, 2 to -5: -7, -10 to -17: -7
So next would be: -34 - 7 = -41, then -41 × 2 = -82

Pattern: multiply by 2, subtract 7, multiply by 2, subtract 7...
- 4 × 2 = 8
- 8 - 7 = 1
- 1 × 2 = 2
- 2 - 7 = -5
- -5 × 2 = -10
- -10 - 7 = -17
- -17 × 2 = -34
- -34 - 7 = -41
- -41 × 2 = -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: +6, -7 (alternating)
- 19 + 6 = 25
- 25 - 7 = 18
- 18 + 6 = 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, subtract 6 (alternating)
- -34 × 2 = -68
- -68 - 6 = -74
- -74 × 2 = -148

Now let me go back to Series 2 and work it out more carefully:

Series 2: 1, 3, -1, -3, -7, -21, -25, __, __, __

Let me try different approaches:
Approach 1 - Looking at operations:
1 → 3 (+2)
3 → -1 (-4)
-1 → -3 (-2)
-3 → -7 (-4)
-7 → -21 (-14 or ×3)
-21 → -25 (-4)

The -4 appears multiple times. Let me see if there's a pattern with ×3:
-7 × 3 = -21 ✓

So maybe: +2, -4, -2, -4, ×3, -4, ...

If we continue: -25 × 3 = -75, then -75 - 4 = -79, then -79 × 3 = -237

Let me verify: 1, 3, -1, -3, -7, -21, -25, -75, -79, -237

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