Patterns Worksheets | Dynamically Created Patterns Worksheets - Free Printable

Let's solve each of these numerical series step by step and explain the pattern.

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1) 4, 8, 10, 20, 22, 44, 46, __, __, __

Step-by-step analysis:
- 4 → 8 (×2)
- 8 → 10 (+2)
- 10 → 20 (×2)
- 20 → 22 (+2)
- 22 → 44 (×2)
- 44 → 46 (+2)

Pattern: Alternating ×2 and +2

So:
- 46 → ? (×2) = 92
- 92 → ? (+2) = 94
- 94 → ? (×2) = 188

✔ Answer: 92, 94, 188

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2) 1, 3, -1, -3, -7, -21, -25, __, __, __

Check differences or patterns:

- 1 → 3 (+2)
- 3 → -1 (-4)
- -1 → -3 (-2)
- -3 → -7 (-4)
- -7 → -21 (-14)
- -21 → -25 (-4)

Wait, this seems messy. Let's look at groups:

Try splitting into two interleaved sequences?

Odd positions: 1, -1, -7, -25
Even positions: 3, -3, -21, ?

But maybe not.

Alternatively, check if it's a recursive pattern.

Another idea: Look at the changes:

- 1 to 3: +2
- 3 to -1: -4
- -1 to -3: -2
- -3 to -7: -4
- -7 to -21: -14
- -21 to -25: -4

Hmm, alternating between -4 and other values?

Wait:
+2, -4, -2, -4, -14, -4

No clear pattern.

Wait — let's try grouping:

Look at pairs:

(1, 3), (-1, -3), (-7, -21), (-25, ?)

From first pair: 1 → 3 (×3? No, +2)

Wait — perhaps look at how each term is generated.

Try this:

- 1 → 3: ×3 - 0?
- 3 → -1: Not obvious.

Wait — another idea: alternating operations

Try:
- Start: 1
- 1 × 3 = 3
- 3 - 4 = -1
- -1 × 3 = -3
- -3 - 4 = -7
- -7 × 3 = -21
- -21 - 4 = -25
- -25 × 3 = -75
- -75 - 4 = -79
- -79 × 3 = -237

Yes! Pattern: ×3, then -4, repeating.

So:
- After -25: ×3 = -75
- Then -4 = -79
- Then ×3 = -237

✔ Answer: -75, -79, -237

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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, 2, 3, 5, 8
- Next: 5 + 8 = 13
- Then: 8 + 13 = 21
- Then: 13 + 21 = 34

✔ Answer: 13, 21, 34

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

Check the 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

So pattern: ×3, +4, ×3, +4, ...

✔ Answer: 480, 484, 1452

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

Split into two interleaved sequences:

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

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

So next three terms are:

- 8th position: 6
- 9th: next odd → 1
- 10th: even → 4 (since 6 - 2 = 4)

Sequence:
Positions:
1: 9
2: 12
3: 7
4: 10
5: 5
6: 8
7: 3
8: ? → 6
9: ? → 1
10: ? → 4

So the blanks are: 6, 1, 4

✔ Answer: 6, 1, 4

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

Look at positions:

Group in threes?

Or split into two sequences?

Try odd and even positions:

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

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

Now list:

- 1: 16
- 2: 22
- 3: 19
- 4: 25
- 5: 22
- 6: 28
- 7: 25
- 8: ? → 31
- 9: ? → 28 (odd sequence)
- 10: ? → 34 (even sequence)

So:
- 8th: 31
- 9th: 28
- 10th: 34

✔ Answer: 31, 28, 34

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

This is identical to #4, so same pattern:

×3, +4, ×3, +4...

We already did:

- 160 → ×3 = 480
- 480 → +4 = 484
- 484 → ×3 = 1452

✔ Answer: 480, 484, 1452

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

Check differences:

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

Not consistent.

Try splitting into two sequences?

Odd positions (1st, 3rd, 5th, 7th): 4, 1, -5, -17

Check:
- 4 → 1: -3
- 1 → -5: -6
- -5 → -17: -12 → difference: -3, -6, -12 → doubling?

Next: -24 → so -17 -24 = -41

Even positions (2nd, 4th, 6th, 8th): 8, 2, -10, ?

- 8 → 2: -6
- 2 → -10: -12
- -10 → ? → -24 → so -10 -24 = -34

So:
- 8th: -34
- 9th: -41
- 10th: next even → -34 -48 = -82? Wait, pattern?

Wait: Even positions:
- 8 → 2: -6
- 2 → -10: -12
- -10 → ?: -24 → so next: -34

Then next even (10th): -34 -48 = -82? But we need only 3 more terms.

So:
- 8th: -34
- 9th: -41
- 10th: -82? But wait — what’s the pattern?

Odd sequence: 4, 1, -5, -17 → differences: -3, -6, -12 → multiply by 2

So next difference: -24 → -17 -24 = -41

Even sequence: 8, 2, -10 → differences: -6, -12 → next: -24 → -10 -24 = -34

So:
- 8th: -34
- 9th: -41
- 10th: next even → -34 -48 = -82? But we don’t know yet.

Wait, but the pattern for even: -6, -12, -24 → ×2 → next: -48 → so -34 -48 = -82

But we only need 3 blanks: after -17

So:
- 8th: -34
- 9th: -41
- 10th: -82

✔ Answer: -34, -41, -82

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

Split into odd and even:

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

So:
- 8th: 25
- 9th: 18
- 10th: 24 (next even: 25 -1 = 24)

Wait: even positions: 28, 27, 26, 25 → yes

Then next odd: 18

Then next even: 24

So:
- 8th: 25
- 9th: 18
- 10th: 24

✔ Answer: 25, 18, 24

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

Check pattern:

- 1 → 2: +1
- 2 → -4: -6
- -4 → -8: -4
- -8 → -14: -6
- -14 → -28: -14
- -28 → -34: -6

Hmm.

Wait: alternate -6 and something?

- +1, -6, -4, -6, -14, -6

Not clear.

Try splitting into two sequences?

Odd positions: 1, -4, -14, -34

- 1 → -4: -5
- -4 → -14: -10
- -14 → -34: -20 → differences: -5, -10, -20 → ×2 → next: -40 → -34 -40 = -74

Even positions: 2, -8, -28, ?

- 2 → -8: -10
- -8 → -28: -20 → next: -40 → -28 -40 = -68

So:
- 8th: -68 (even)
- 9th: -74 (odd)
- 10th: next even → -68 -80 = -148?

Wait, even sequence: -10, -20, -40 → ×2 → next: -80 → so -68 -80 = -148

But we need only 3 terms.

So:
- 8th: -68
- 9th: -74
- 10th: -148

Wait — let's confirm:

Odd: 1, -4, -14, -34 → diff: -5, -10, -20 → next: -40 → -34 -40 = -74 ✔

Even: 2, -8, -28 → diff: -10, -20 → next: -40 → -28 -40 = -68 ✔

Then next even: -68 -80 = -148

So:
- 8th: -68
- 9th: -74
- 10th: -148

✔ Answer: -68, -74, -148

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## ✔ Final Answers:

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

Let me know if you'd like explanations in a printable format or as a table!