Patterns Worksheets | Dynamically Created Patterns Worksheets - Free Printable

Let’s solve each numerical series one by one. We’ll look for patterns — like adding, subtracting, multiplying, or alternating rules.

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

Look at the steps:
- 4 → 8 (+4)
- 8 → 10 (+2)
- 10 → 20 (×2)
- 20 → 22 (+2)
- 22 → 44 (×2)
- 44 → 46 (+2)

Pattern: +4, +2, ×2, +2, ×2, +2... so next should be ×2, then +2, then ×2?

Wait — let’s check again:

Actually, after 4→8 (+4), it seems to alternate between “+2” and “×2”, but starting from 8:

8 → 10 (+2)
10 → 20 (×2)
20 → 22 (+2)
22 → 44 (×2)
44 → 46 (+2)
So next: 46 × 2 = 92
Then: 92 + 2 = 94
Then: 94 × 2 = 188

✔ Answer: 92, 94, 188

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

Check differences:
1 → 3 (+2)
3 → -1 (-4)
-1 → -3 (-2)
-3 → -7 (-4)
-7 → -21 (×3? or -14?) Wait — -7 to -21 is ×3? But that breaks pattern.

Wait — maybe two interleaved sequences?

Odd positions: 1st, 3rd, 5th, 7th: 1, -1, -7, -25
Even positions: 2nd, 4th, 6th: 3, -3, -21

Look at odd:
1 → -1 (-2)
-1 → -7 (-6)
-7 → -25 (-18) → differences: -2, -6, -18 → each time ×3? So next difference: -54 → -25 -54 = -79

Even:
3 → -3 (-6)
-3 → -21 (-18) → same pattern: -6, -18 → next -54 → -21 -54 = -75

But we need to fill in order: position 8 (even), 9 (odd), 10 (even)

So:
8th term (even): -21 -54 = -75
9th term (odd): -25 -54 = -79
10th term (even): -75 - (54×3=162) → wait, no — the multiplier was ×3 on the *difference*, not the term.

Actually, the differences in even sequence: -6, -18 → next is -54 → so -21 + (-54) = -75
Then next even would be -75 + (-162) = -237? But we only need up to 10th.

Wait — let's list with indices:

Term 1: 1
Term 2: 3
Term 3: -1
Term 4: -3
Term 5: -7
Term 6: -21
Term 7: -25
Term 8: ?
Term 9: ?
Term 10: ?

From term 5 to 6: -7 to -21 → that’s ×3? Or -14? Doesn’t fit.

Alternative idea: Maybe group as pairs?

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

In first pair: 1×3=3
Second: -1×3=-3
Third: -7×3=-21
Fourth: -25×3=-75

So term 8 = -75

Now what about term 9? After -25, how did we get to -25? From previous odd terms: 1, -1, -7, -25

1 to -1: -2
-1 to -7: -6
-7 to -25: -18 → which is -2×3, -6×3, -18×3 → next difference: -54 → -25 -54 = -79

Then term 10: since term 8 is -75, and if pattern holds, term 10 should be term 8 ×3? No — term 8 is already result of ×3.

Actually, looking back: every even term is 3 times the preceding odd term.

Term 2 = 3 × term 1 → 3×1=3 ✔️
Term 4 = 3 × term 3 → 3×(-1)=-3 ✔️
Term 6 = 3 × term 5 → 3×(-7)=-21 ✔️
Term 8 = 3 × term 7 → 3×(-25)=-75 ✔️

Now term 9: follows the odd-term pattern: 1, -1, -7, -25,...

Differences: -2, -6, -18 → each multiplied by 3 → next difference: -54 → -25 + (-54) = -79

Term 10 = 3 × term 9 = 3 × (-79) = -237

✔ Answer: -75, -79, -237

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

This is Fibonacci! Each number is sum of two before.

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

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

Check steps:
4 → 12 (×3)
12 → 16 (+4)
16 → 48 (×3)
48 → 52 (+4)
52 → 156 (×3)
156 → 160 (+4)
So next: 160 ×3 = 480
Then: 480 +4 = 484
Then: 484 ×3 = 1452

✔ Answer: 480, 484, 1452

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

Alternating operations?

9 → 12 (+3)
12 → 7 (-5)
7 → 10 (+3)
10 → 5 (-5)
5 → 8 (+3)
8 → 3 (-5)
So next: 3 +3 = 6
Then: 6 -5 = 1
Then: 1 +3 = 4

✔ Answer: 6, 1, 4

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

Look at changes:
16 → 22 (+6)
22 → 19 (-3)
19 → 25 (+6)
25 → 22 (-3)
22 → 28 (+6)
28 → 25 (-3)
So next: 25 +6 = 31
Then: 31 -3 = 28
Then: 28 +6 = 34

✔ Answer: 31, 28, 34

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

Same as #4! Probably a duplicate.

As above: ×3, +4, ×3, +4,...

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, __, __, __

Group in pairs?

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

First of each pair: 4, 1, -5, -17
Second: 8, 2, -10, ?

Look at first numbers:
4 → 1 (-3)
1 → -5 (-6)
-5 → -17 (-12) → differences: -3, -6, -12 → each ×2 → next difference: -24 → -17 -24 = -41

Second numbers:
8 → 2 (-6)
2 → -10 (-12)
-10 → ? → next difference: -24 → -10 -24 = -34

But also notice: second number is double the first in each pair?

4×2=8 ✔️
1×2=2 ✔️
-5×2=-10 ✔️
So -17×2 = -34 ✔️

So term 8 = -34
Term 9 = next first number = -41
Term 10 = -41 ×2 = -82

Wait — sequence is: term7 is -17, so term8 should be its pair: -34
Then term9 is next first number: -41
Term10 is its pair: -82

✔ Answer: -34, -41, -82

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

Changes:
22 → 28 (+6)
28 → 21 (-7)
21 → 27 (+6)
27 → 20 (-7)
20 → 26 (+6)
26 → 19 (-7)
So next: 19 +6 = 25
Then: 25 -7 = 18
Then: 18 +6 = 24

✔ Answer: 25, 18, 24

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

Look at steps:
1 → 2 (+1)
2 → -4 (-6)
-4 → -8 (-4)
-8 → -14 (-6)
-14 → -28 (-14? or ×2?) → -14×2 = -28 ✔️
-28 → -34 (-6)
Hmm — inconsistent.

Try grouping:

(1,2), (-4,-8), (-14,-28), (-34, ?)

First of pair: 1, -4, -14, -34
Second: 2, -8, -28, ?

Notice second is double first: 1×2=2, -4×2=-8, -14×2=-28 → so -34×2 = -68

Now first numbers: 1, -4, -14, -34
Differences:
1 to -4: -5
-4 to -14: -10
-14 to -34: -20 → each difference ×2 → next difference: -40 → -34 -40 = -74

So term 8 = -68 (double of -34)
Term 9 = -74 (next first number)
Term 10 = -74 ×2 = -148

✔ Answer: -68, -74, -148

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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