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 — to find the next three numbers.

---

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

Look at how we get from one number to the next:

- 4 → 8 (×2)
- 8 → 10 (+2)
- 10 → 20 (×2)
- 20 → 22 (+2)
- 22 → 44 (×2)
- 44 → 46 (+2)

Pattern: ×2, +2, ×2, +2, ×2, +2...

So next:
- 46 × 2 = 92
- 92 + 2 = 94
- 94 × 2 = 188

✔ Answer: 92, 94, 188

---

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

Check differences or operations:

From 1 → 3: +2
3 → -1: -4
-1 → -3: -2
-3 → -7: -4
-7 → -21: ×3? Wait, that breaks pattern. Let’s try grouping:

Maybe two interleaved sequences?

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

Wait — let’s check another way:

Try this:
Start with 1
Then 1 × 3 = 3
Then 3 - 4 = -1
Then -1 × 3 = -3
Then -3 - 4 = -7
Then -7 × 3 = -21
Then -21 - 4 = -25

Ah! Pattern: ×3, -4, ×3, -4, ×3, -4...

So next:
- -25 × 3 = -75
- -75 - 4 = -79
- -79 × 3 = -237

✔ Answer: -75, -79, -237

---

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

This is famous — Fibonacci sequence!

Each number is sum of previous two:

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

---

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

Pattern: ×3, +4, ×3, +4, ×3, +4...

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

✔ Answer: 480, 484, 1452

*(Note: Problem #7 is identical — same answer)*

---

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

Look at changes:

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

Pattern: +3, -5, +3, -5, +3, -5...

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

✔ Answer: 6, 1, 4

---

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

Changes:

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

Pattern: +6, -3, +6, -3, +6, -3...

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

✔ Answer: 31, 28, 34

---

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

Same as problem #4 → already solved.

✔ Answer: 480, 484, 1452

---

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

Break into pairs? Or look at differences:

4 → 8: +4
8 → 1: -7
1 → 2: +1
2 → -5: -7
-5 → -10: -5? Not matching.

Wait — maybe group in threes?

Another idea: Look at every other term?

Or perhaps:

First pair: 4, 8 → then 1, 2 → then -5, -10 → then -17, ?

Notice:

4 → 8 (×2)
Then 8 → 1 (-7)
1 → 2 (×2)
2 → -5 (-7)
-5 → -10 (×2)
-10 → -17 (-7)

Pattern: ×2, -7, ×2, -7, ×2, -7...

So after -17:

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

✔ Answer: -34, -41, -82

---

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

Pattern: +6, -7, +6, -7, +6, -7...

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

✔ Answer: 25, 18, 24

---

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

Check steps:

1 → 2: ×2
2 → -4: ×(-2)? Or -6? Let’s see:

Actually:

1 → 2: +1? No.

Wait:

1 → 2: ×2
2 → -4: ×(-2)
-4 → -8: ×2
-8 → -14: -6? Doesn’t fit.

Alternative approach:

Group:

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

In each pair, second is double first:

1×2=2
-4×2=-8
-14×2=-28
So next pair starts with -34 → next should be -34×2 = -68

But what connects the pairs?

After 2 → -4: difference of -6
After -8 → -14: difference of -6
After -28 → -34: difference of -6

Yes! So between end of one pair and start of next: subtract 6.

Sequence:

Pair 1: 1, 2
Then 2 - 6 = -4 → Pair 2: -4, -8
Then -8 - 6 = -14 → Pair 3: -14, -28
Then -28 - 6 = -34 → Pair 4: -34, -68
Then -68 - 6 = -74 → Pair 5: -74, -148

Wait — but we only need next three after -34.

So:

After -34:
→ -34 × 2 = -68
→ Then -68 - 6 = -74
→ Then -74 × 2 = -148

✔ Answer: -68, -74, -148

---

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