Patterns Worksheets | Dynamically Created Patterns Worksheets - Free Printable

Let's solve each numerical series one by one, explaining the pattern for each.

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1) 4, 8, 10, 20, 22, 44, __, __, __

Pattern:
Alternate operations:
- ×2, then +2, then ×2, then +2, etc.

Breakdown:
4 → ×2 → 8
8 → +2 → 10
10 → ×2 → 20
20 → +2 → 22
22 → ×2 → 44
44 → +2 → 46
46 → ×2 → 92
92 → +2 → 94

✔ Answer: 46, 92, 94

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2) 1, 3, -1, -3, -7, -21, __, __, __

This looks tricky. Let’s look at the operations:

1 → 3: ×3? But 1×3=3 ✔️
3 → -1: 3 - 4 = -1
-1 → -3: ×3? -1×3 = -3 ✔️
-3 → -7: -3 - 4 = -7
-7 → -21: ×3? -7×3 = -21 ✔️

So pattern: ×3, then -4, repeat

Next:
-21 → -4 → -25
-25 → ×3 → -75
-75 → -4 → -79

✔ Answer: -25, -75, -79

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3) 0, 1, 1, 2, 3, 5, 8, __, __, __

Classic Fibonacci sequence: Each number is sum of two before it.

0, 1 → 1 (0+1)
1, 1 → 2 (1+1)
1, 2 → 3 (1+2)
2, 3 → 5
3, 5 → 8
5, 8 → 13
8, 13 → 21
13, 21 → 34

✔ Answer: 13, 21, 34

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4) 4, 12, 16, 48, 52, 156, 160, __, __, __

Look at pattern:

4 → ×3 → 12
12 → +4 → 16
16 → ×3 → 48
48 → +4 → 52
52 → ×3 → 156
156 → +4 → 160
160 → ×3 → 480
480 → +4 → 484
484 → ×3 → 1452

✔ Answer: 480, 484, 1452

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5) 9, 12, 7, 10, 5, 8, 3, __, __, __

Group as pairs:
(9,12), (7,10), (5,8), (3,?)

In each pair: second = first + 3
9→12 (+3), 7→10 (+3), 5→8 (+3), so 3→6

Now look at first elements: 9, 7, 5, 3 → decreasing by 2
Next first element would be 1 → then 1+3=4

Then next: -1 → -1+3=2

But we need only 3 more terms: after 3, we have:

3 → 6 (from pair rule)
Then next pair starts with 1 → 1, 4? Wait — let’s list all:

Sequence: 9, 12, 7, 10, 5, 8, 3, 6, 1, 4

Yes! Alternating: odd positions decrease by 2: 9,7,5,3,1
Even positions: 12,10,8,6,4 — also decreasing by 2.

So after 3 (position 7), position 8 = 6, position 9 = 1, position 10 = 4.

✔ Answer: 6, 1, 4

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6) 16, 22, 19, 25, 22, 28, 25, __, __, __

Pattern: Two interleaved sequences.

Odd positions (1st,3rd,5th,7th): 16, 19, 22, 25 → +3 each time → next: 28

Even positions (2nd,4th,6th,8th): 22, 25, 28 → +3 → next: 31

Then next odd: 28 → 31? Wait — let’s index:

Pos 1: 16
Pos 2: 22
Pos 3: 19
Pos 4: 25
Pos 5: 22
Pos 6: 28
Pos 7: 25
Pos 8: ? → even → 28 + 3 = 31
Pos 9: ? → odd → 25 + 3 = 28
Pos 10: ? → even → 31 + 3 = 34

✔ Answer: 31, 28, 34

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7) 4, 12, 16, 48, 52, 156, 160, __, __, __

Wait — this is identical to problem #4!

Same pattern: ×3, +4, ×3, +4...

We already solved it:

After 160 → ×3 → 480
→ +4 → 484
→ ×3 → 1452

✔ Answer: 480, 484, 1452

*(Note: Probably a duplicate or copy-paste error in worksheet)*

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8) 4, 8, 1, 2, -5, -10, -17, __, __, __

Let’s look at differences:

4 → 8: +4
8 → 1: -7
1 → 2: +1
2 → -5: -7
-5 → -10: -5
-10 → -17: -7

Not consistent. Try grouping:

(4,8), (1,2), (-5,-10), (-17,?)

In each pair: second = first ×2?
4×2=8 ✔️
1×2=2 ✔️
-5×2=-10 ✔️
-17×2=-34

Now look at first elements of pairs: 4, 1, -5, -17

Differences:
4 → 1: -3
1 → -5: -6
-5 → -17: -12 → which is -3, -6, -12 → doubling the subtraction?

Next subtraction: -24 → -17 -24 = -41

Then pair: -41 → ×2 = -82

So next three terms: -34 (from -17×2), then -41, then -82

Sequence: ... -17, -34, -41, -82

✔ Answer: -34, -41, -82

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9) 22, 28, 21, 27, 20, 26, 19, __, __, __

Two interleaved sequences:

Odd positions (1st,3rd,5th,7th): 22, 21, 20, 19 → decreasing by 1 → next: 18

Even positions (2nd,4th,6th,8th): 28, 27, 26 → decreasing by 1 → next: 25

Then next odd: 18 → 17

So after 19 (pos 7), pos 8 = 25, pos 9 = 18, pos 10 = 24? Wait:

List:

Pos 1: 22
Pos 2: 28
Pos 3: 21
Pos 4: 27
Pos 5: 20
Pos 6: 26
Pos 7: 19
Pos 8: 25 (even, 26-1)
Pos 9: 18 (odd, 19-1)
Pos 10: 24 (even, 25-1)

✔ Answer: 25, 18, 24

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10) 1, 2, -4, -8, -14, -28, -34, __, __, __

Look at pattern:

1 → 2: ×2
2 → -4: -6?
-4 → -8: ×2
-8 → -14: -6
-14 → -28: ×2
-28 → -34: -6
-34 → ×2 → -68
-68 → -6 → -74
-74 → ×2 → -148

Pattern: ×2, then -6, repeat.

✔ Answer: -68, -74, -148

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## ✔ Final Answers:

1) 46, 92, 94
2) -25, -75, -79
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

Let me know if you’d like these written in a printable format or with diagrams!