Patterns Worksheets | Dynamically Created Patterns Worksheets - Free Printable

Let’s solve each numerical series one by one, identifying the pattern and filling in the next three missing terms.

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

Pattern:
- ×2, +2, ×2, +2, ×2, +2...

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, __, __, __

Pattern:
This looks like alternating operations. Let’s look at differences or groupings:

From 1 → 3: +2
3 → -1: -4
-1 → -3: -2
-3 → -7: -4
-7 → -21: ×3? (But -7×3 = -21 — that fits!)

Wait — let's try grouping:

Group 1: 1, 3 → maybe multiply by 3? 1×3=3
Then 3 → -1: subtract 4?
-1 → -3: subtract 2?
-3 → -7: subtract 4?
-7 → -21: multiply by 3?

So pattern might be:
×3, -4, -2, -4, ×3, -4, -2, -4, ×3...

Check:

Start: 1
×3 → 3
-4 → -1
-2 → -3
-4 → -7
×3 → -21
-4 → -25
-2 → -27
-4 → -31

✔ Answer: -25, -27, -31

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

This is the Fibonacci sequence!

Each term is sum of two previous:

0, 1, 1 (0+1), 2 (1+1), 3 (1+2), 5 (2+3), 8 (3+5)

Next:
- 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 → 12: ×3
12 → 16: +4
16 → 48: ×3
48 → 52: +4
52 → 156: ×3
156 → 160: +4
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, __, __, __

Pattern: Alternating sequences?

Split into odd and even positions:

Odd positions (1st, 3rd, 5th, 7th): 9, 7, 5, 3 → decreasing by 2

Even positions (2nd, 4th, 6th): 12, 10, 8 → decreasing by 2

So next:

8th term (even position): 8 - 2 = 6

9th term (odd position): 3 - 2 = 1

10th term (even position): 6 - 2 = 4

✔ Answer: 6, 1, 4

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

Again, split into two interleaved sequences:

Odd positions: 16, 19, 22, 25 → +3 each time → next: 28

Even positions: 22, 25, 28 → +3 each time → next: 31

Sequence so far: pos1=16, pos2=22, pos3=19, pos4=25, pos5=22, pos6=28, pos7=25, pos8=?, pos9=?, pos10=?

So:
- pos8 (even): 28 + 3 = 31
- pos9 (odd): 25 + 3 = 28
- pos10 (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 numbers.

So same pattern: ×3, +4, ×3, +4, etc.

We already solved it:

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

✔ Answer: 480, 484, 1452

*(Note: Probably a duplicate in the worksheet.)*

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

Look at differences:

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

Hmm, not clear. Try grouping:

Group 1: 4, 8 → ×2
Group 2: 1, 2 → ×2
Group 3: -5, -10 → ×2
Group 4: -17, ? → ×2 → -34

But then what about the transitions?

Between groups: 8 → 1: -7
2 → -5: -7
-10 → -17: -7

Ah! Pattern:

Start with 4
→ ×2 = 8
→ -7 = 1
→ ×2 = 2
→ -7 = -5
→ ×2 = -10
→ -7 = -17
→ ×2 = -34
→ -7 = -41
→ ×2 = -82

✔ Answer: -34, -41, -82

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

Split into two sequences:

Odd positions: 22, 21, 20, 19 → decreasing by 1 → next: 18

Even positions: 28, 27, 26 → decreasing by 1 → next: 25

So:

pos8 (even): 25
pos9 (odd): 18
pos10 (even): 24

✔ 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, -6, ×2, -6, ...

✔ Answer: -68, -74, -148

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## ✔ Final Answers:

1) 46, 92, 94
2) -25, -27, -31
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 a visual chart or explanation for any specific one!