Patterns Worksheets | Dynamically Created Patterns Worksheets - Free Printable

Let’s go through each number series one by one. We’ll look for patterns — like adding, subtracting, multiplying, or alternating operations — to find the next three numbers in each.

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

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

So the pattern is: ×2, +2, ×2, +2, ...

Next:
- 46 × 2 = 92
- 92 + 2 = 94
- 94 × 2 = 188

✔ Next three: 92, 94, 188

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

Let’s check differences:
- 1 → 3: +2
- 3 → -1: -4
- -1 → -3: -2
- -3 → -7: -4
- -7 → -21: -14? Hmm, not consistent.

Wait — maybe group them?

Try this:
- 1 → 3: +2
- 3 → -1: -4
- -1 → -3: -2
- -3 → -7: -4
- -7 → -21: -14? That breaks it.

Alternative idea: Maybe two alternating sequences?

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

Check odd positions:
1 → -1: -2
-1 → -7: -6
-7 → -25: -18
Differences: -2, -6, -18 → each time ×3? So next difference: -54 → -25 -54 = -79

Even positions:
3 → -3: -6
-3 → -21: -18
Next: -18 ×3 = -54 → -21 -54 = -75

But we need next three terms after -25 (which is position 7).

Positions:
1: 1
2: 3
3: -1
4: -3
5: -7
6: -21
7: -25 ← current last
8: ? (even position) → should be -75
9: ? (odd position) → -79
10: ? (even) → -75 -54×3? Wait, let’s recheck.

Actually, let’s try another approach.

Look at pairs:

(1, 3) → 1+2=3
(-1, -3) → -1-2=-3
(-7, -21) → -7×3=-21
(-25, ?) → maybe -25-2 = -27? But that doesn’t fit.

Wait — perhaps:

From 1 to 3: +2
3 to -1: -4
-1 to -3: -2
-3 to -7: -4
-7 to -21: -14? No.

Another idea: Maybe it’s two interleaved sequences with different rules.

Sequence A (positions 1,3,5,7): 1, -1, -7, -25
Differences: -2, -6, -18 → each ×3 → next diff: -54 → -25 -54 = -79

Sequence B (positions 2,4,6,8): 3, -3, -21, ?
Differences: -6, -18 → next: -54 → -21 -54 = -75

Then position 9 is Sequence A: -79
Position 10 is Sequence B: -75 -54×3? Wait no — if differences are ×3 each time:

Sequence B:
3 → -3: -6
-3 → -21: -18 (= -6 ×3)
-21 → ?: -54 (= -18 ×3) → so ? = -21 -54 = -75

Then next in Sequence A: -25 -54 = -79
Then next in Sequence B: -75 -162? No — wait, we only need next three after -25.

After -25 (position 7), next are:

Position 8: Sequence B → -75
Position 9: Sequence A → -79
Position 10: Sequence B → -75 - 162? Wait, no — the multiplier is on the *difference*, not the value.

Sequence B differences: -6, -18, then next difference should be -54 (since -18 ×3 = -54)

So from -21, subtract 54 → -75 (that’s position 8)

Then position 9: Sequence A: from -25, subtract 54 → -79

Then position 10: Sequence B: from -75, subtract 162? Wait — no, the next difference after -54 would be -162? But we don’t need that yet.

We only need next three after -25: positions 8,9,10.

So:

Pos 8: -75
Pos 9: -79
Pos 10: next in Sequence B: -75 - 162? Let’s see the pattern of differences in B: -6, -18, -54 → yes, each ×3.

So after -54, next difference is -162 → -75 -162 = -237

But that seems too big. Let me double-check.

Actually, let’s list all:

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

If Sequence A (odd pos): 1, -1, -7, -25, ?
Diffs: -2, -6, -18 → next diff: -54 → -25 -54 = -79

Sequence B (even pos): 3, -3, -21, ?
Diffs: -6, -18 → next diff: -54 → -21 -54 = -75

Then pos 9 is Sequence A: -79
Pos 10 is Sequence B: -75 - 162? No — the next diff for B after -54 is -162, but we only need up to pos 10, which is the first term of the next pair? Actually, pos 8 is B, pos 9 is A, pos 10 is B again? No:

Positions:
1: A
2: B
3: A
4: B
5: A
6: B
7: A
8: B
9: A
10: B

So after pos 7 (A: -25), next is pos 8 (B: -75), then pos 9 (A: -79), then pos 10 (B: -75 - 162? Wait, no — the difference for B is applied to get the next B term.

From pos 6 (B: -21) to pos 8 (B: ?): difference is -54 → -21 -54 = -75

Then from pos 8 (B: -75) to pos 10 (B: ?): next difference is -162 → -75 -162 = -237

But that seems excessive. Maybe I made a mistake.

Alternative approach: Look at the entire sequence:

1, 3, -1, -3, -7, -21, -25

Notice:
1 to 3: +2
3 to -1: -4
-1 to -3: -2
-3 to -7: -4
-7 to -21: -14? Not good.

Another idea: Perhaps it's two sequences combined with multiplication and addition.

Let’s try:

Start with 1
+2 = 3
-4 = -1
-2 = -3
-4 = -7
-14 = -21? No.

Wait — what if it's:

1
1 + 2 = 3
3 - 4 = -1
-1 - 2 = -3
-3 - 4 = -7
-7 - 14 = -21? No.

Perhaps it's based on previous two numbers.

Let’s give up and use the interleaved method since it worked for the first few.

So for problem 2, using interleaved sequences:

Sequence A (odd indices): 1, -1, -7, -25, -79, ...
Sequence B (even indices): 3, -3, -21, -75, -237, ...

So after -25 (which is index 7, A), next are:

Index 8 (B): -75
Index 9 (A): -79
Index 10 (B): -237

But -237 seems too large. Let me verify with another method.

Look at the sequence: 1, 3, -1, -3, -7, -21, -25

Notice that from 3 to -1: -4
-1 to -3: -2
-3 to -7: -4
-7 to -21: -14? No.

Another thought: Maybe it's -2, -2, -4, -14, -4? Doesn't help.

Let’s calculate the differences between consecutive terms:

3 - 1 = 2
-1 - 3 = -4
-3 - (-1) = -2
-7 - (-3) = -4
-21 - (-7) = -14
-25 - (-21) = -4

So differences: +2, -4, -2, -4, -14, -4

Not obvious.

Perhaps it's two sequences: one for odd positions, one for even, and they have their own patterns.

Odd positions: 1, -1, -7, -25
As before: 1 to -1: -2
-1 to -7: -6
-7 to -25: -18
-2 to -6: ×3, -6 to -18: ×3, so next -18×3 = -54, so -25 -54 = -79

Even positions: 3, -3, -21, ?
3 to -3: -6
-3 to -21: -18
-6 to -18: ×3, so next -18×3 = -54, so -21 -54 = -75

Then the next even position after that would be -75 -162 = -237, but for our purpose, after -25 (position 7), the next three are positions 8,9,10:

Pos 8: even sequence next term: -75
Pos 9: odd sequence next term: -79
Pos 10: even sequence next term: -75 -162 = -237? But that's for pos 10, which is even, so yes.

But let's confirm the indexing:

Position 1: 1 (A)
2: 3 (B)
3: -1 (A)
4: -3 (B)
5: -7 (A)
6: -21 (B)
7: -25 (A)
8: ? (B) -> -75
9: ? (A) -> -79
10: ? (B) -> -237

Yes.

So for problem 2: -75, -79, -237

But I feel like -237 might be wrong because the jump is large. Let me see if there's a better pattern.

Another idea: Perhaps the sequence is generated by a rule like:

Start with 1
Then 1 + 2 = 3
Then 3 - 4 = -1
Then -1 - 2 = -3
Then -3 - 4 = -7
Then -7 - 14 = -21? Why 14?

Notice that 2,4,2,4,14,4 — not clear.

Perhaps it's related to the position.

Let’s move on and come back if needed. For now, I'll stick with the interleaved method.

So for 2): -75, -79, -237

But let's write it as:

After -25, next is -75 (B), then -79 (A), then -237 (B)

Yes.

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

This is the Fibonacci sequence! Each number is the sum of the two before it.

0+1=1
1+1=2
1+2=3
2+3=5
3+5=8
5+8=13
8+13=21
13+21=34

✔ Next three: 13, 21, 34

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

Look at the pattern:

4 → 12: ×3
12 → 16: +4
16 → 48: ×3
48 → 52: +4
52 → 156: ×3
156 → 160: +4

So pattern: ×3, +4, ×3, +4, ...

Next:
160 × 3 = 480
480 + 4 = 484
484 × 3 = 1452

✔ Next three: 480, 484, 1452

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

Look at the pattern:

9 → 12: +3
12 → 7: -5
7 → 10: +3
10 → 5: -5
5 → 8: +3
8 → 3: -5

So pattern: +3, -5, +3, -5, +3, -5, ...

Next:
3 + 3 = 6
6 - 5 = 1
1 + 3 = 4

✔ Next three: 6, 1, 4

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

Look at the pattern:

16 → 22: +6
22 → 19: -3
19 → 25: +6
25 → 22: -3
22 → 28: +6
28 → 25: -3

So pattern: +6, -3, +6, -3, +6, -3, ...

Next:
25 + 6 = 31
31 - 3 = 28
28 + 6 = 34

✔ Next three: 31, 28, 34

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

This is the same as problem 4!

Pattern: ×3, +4, ×3, +4, ...

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

✔ Next three: 480, 484, 1452

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

Look at the pattern:

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

So pattern: ×2, -7, ×2, -7, ×2, -7, ...

Next:
-17 × 2 = -34
-34 - 7 = -41
-41 × 2 = -82

✔ Next three: -34, -41, -82

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

Look at the pattern:

22 → 28: +6
28 → 21: -7
21 → 27: +6
27 → 20: -7
20 → 26: +6
26 → 19: -7

So pattern: +6, -7, +6, -7, +6, -7, ...

Next:
19 + 6 = 25
25 - 7 = 18
18 + 6 = 24

✔ Next three: 25, 18, 24

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

Look at the pattern:

1 → 2: +1? Or ×2? 1×2=2
2 → -4: ×(-2)
-4 → -8: ×2
-8 → -14: -6? Not consistent.

Differences:
2 - 1 = 1
-4 - 2 = -6
-8 - (-4) = -4
-14 - (-8) = -6
-28 - (-14) = -14
-34 - (-28) = -6

Not clear.

Another idea: Perhaps alternating operations.

1 to 2: ×2
2 to -4: ×(-2)
-4 to -8: ×2
-8 to -14: -6? No.

Notice:

1, 2, -4, -8, -14, -28, -34

Group as pairs:

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

In each pair, second is double the first? 1×2=2, -4×2=-8, -14×2=-28, so next should be -34×2 = -68

But then what about the jump from 2 to -4? 2 to -4 is -6
From -8 to -14 is -6
From -28 to -34 is -6

Oh! Look:

After the first number, every second number is decreased by 6.

List:

Pos 1: 1
Pos 2: 2 (1×2)
Pos 3: -4 (2 - 6)
Pos 4: -8 (-4×2)
Pos 5: -14 (-8 -6)
Pos 6: -28 (-14×2)
Pos 7: -34 (-28 -6)
Pos 8: ? (-34×2) = -68
Pos 9: ? (-68 -6) = -74
Pos 10: ? (-74×2) = -148

Yes! Pattern:

- Start with 1
- Then ×2
- Then -6
- Then ×2
- Then -6
- Then ×2
- Then -6
- Then ×2
- Then -6
- Then ×2

So:

Pos 8: -34 × 2 = -68
Pos 9: -68 - 6 = -74
Pos 10: -74 × 2 = -148

✔ Next three: -68, -74, -148

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Now, let's compile all 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

For problem 2, I'm still a bit unsure about -237, but based on the interleaved sequence with differences multiplying by 3, it should be correct.

Let me double-check problem 2 quickly.

Sequence A (odd positions): 1, -1, -7, -25, -79
Diffs: -2, -6, -18, -54 → yes, each ×3

Sequence B (even positions): 3, -3, -21, -75, -237
Diffs: -6, -18, -54, -162 → each ×3

Yes, so -237 is correct.

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

──────────────────────────────────────

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