Patterns Worksheets | Dynamically Created Patterns Worksheets - Free Printable

To solve the numerical series problems, we need to identify the pattern or rule governing each sequence. Let's analyze each series step by step.

---

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

- Pattern Analysis:
- The sequence alternates between multiplying by 2 and adding 2.
- \( 4 \times 2 = 8 \)
- \( 8 + 2 = 10 \)
- \( 10 \times 2 = 20 \)
- \( 20 + 2 = 22 \)
- \( 22 \times 2 = 44 \)
- \( 44 + 2 = 46 \)

- Next Terms:
- \( 46 \times 2 = 92 \)
- \( 92 + 2 = 94 \)
- \( 94 \times 2 = 188 \)

- Answer: \( 92, 94, 188 \)

---

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

- Pattern Analysis:
- The sequence alternates between multiplying by -3 and subtracting 4.
- \( 1 \times -3 = -3 \)
- \( -3 - 4 = -7 \)
- \( -7 \times -3 = 21 \)
- \( 21 - 4 = 17 \)
- \( 17 \times -3 = -51 \)
- \( -51 - 4 = -55 \)

- Next Terms:
- \( -25 \times -3 = 75 \)
- \( 75 - 4 = 71 \)
- \( 71 \times -3 = -213 \)

- Answer: \( 75, 71, -213 \)

---

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

- Pattern Analysis:
- This is the Fibonacci sequence, where each term is the sum of the two preceding terms.
- \( 0 + 1 = 1 \)
- \( 1 + 1 = 2 \)
- \( 1 + 2 = 3 \)
- \( 2 + 3 = 5 \)
- \( 3 + 5 = 8 \)

- Next Terms:
- \( 5 + 8 = 13 \)
- \( 8 + 13 = 21 \)
- \( 13 + 21 = 34 \)

- Answer: \( 13, 21, 34 \)

---

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

- Pattern Analysis:
- The sequence alternates between multiplying by 3 and adding 4.
- \( 4 \times 3 = 12 \)
- \( 12 + 4 = 16 \)
- \( 16 \times 3 = 48 \)
- \( 48 + 4 = 52 \)
- \( 52 \times 3 = 156 \)
- \( 156 + 4 = 160 \)

- Next Terms:
- \( 160 \times 3 = 480 \)
- \( 480 + 4 = 484 \)
- \( 484 \times 3 = 1452 \)

- Answer: \( 480, 484, 1452 \)

---

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

- Pattern Analysis:
- The sequence alternates between adding 3 and subtracting 5.
- \( 9 + 3 = 12 \)
- \( 12 - 5 = 7 \)
- \( 7 + 3 = 10 \)
- \( 10 - 5 = 5 \)
- \( 5 + 3 = 8 \)
- \( 8 - 5 = 3 \)

- Next Terms:
- \( 3 + 3 = 6 \)
- \( 6 - 5 = 1 \)
- \( 1 + 3 = 4 \)

- Answer: \( 6, 1, 4 \)

---

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

- Pattern Analysis:
- The sequence alternates between adding 6 and subtracting 3.
- \( 16 + 6 = 22 \)
- \( 22 - 3 = 19 \)
- \( 19 + 6 = 25 \)
- \( 25 - 3 = 22 \)
- \( 22 + 6 = 28 \)
- \( 28 - 3 = 25 \)

- Next Terms:
- \( 25 + 6 = 31 \)
- \( 31 - 3 = 28 \)
- \( 28 + 6 = 34 \)

- Answer: \( 31, 28, 34 \)

---

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

- Pattern Analysis:
- This is the same as Series 4. The sequence alternates between multiplying by 3 and adding 4.
- \( 4 \times 3 = 12 \)
- \( 12 + 4 = 16 \)
- \( 16 \times 3 = 48 \)
- \( 48 + 4 = 52 \)
- \( 52 \times 3 = 156 \)
- \( 156 + 4 = 160 \)

- Next Terms:
- \( 160 \times 3 = 480 \)
- \( 480 + 4 = 484 \)
- \( 484 \times 3 = 1452 \)

- Answer: \( 480, 484, 1452 \)

---

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

- Pattern Analysis:
- The sequence alternates between dividing by 2 and subtracting 7.
- \( 4 \div 2 = 2 \)
- \( 8 - 7 = 1 \)
- \( 1 \div 2 = 0.5 \)
- \( 2 - 7 = -5 \)
- \( -5 \div 2 = -2.5 \)
- \( -10 - 7 = -17 \)

- Next Terms:
- \( -17 \div 2 = -8.5 \)
- \( -10 - 7 = -17 \)
- \( -17 \div 2 = -8.5 \)

- Answer: \( -8.5, -17, -8.5 \)

---

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

- Pattern Analysis:
- The sequence alternates between adding 6 and subtracting 7.
- \( 22 + 6 = 28 \)
- \( 28 - 7 = 21 \)
- \( 21 + 6 = 27 \)
- \( 27 - 7 = 20 \)
- \( 20 + 6 = 26 \)
- \( 26 - 7 = 19 \)

- Next Terms:
- \( 19 + 6 = 25 \)
- \( 25 - 7 = 18 \)
- \( 18 + 6 = 24 \)

- Answer: \( 25, 18, 24 \)

---

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

- Pattern Analysis:
- The sequence alternates between multiplying by 2 and subtracting 6.
- \( 1 \times 2 = 2 \)
- \( 2 - 6 = -4 \)
- \( -4 \times 2 = -8 \)
- \( -8 - 6 = -14 \)
- \( -14 \times 2 = -28 \)
- \( -28 - 6 = -34 \)

- Next Terms:
- \( -34 \times 2 = -68 \)
- \( -68 - 6 = -74 \)
- \( -74 \times 2 = -148 \)

- Answer: \( -68, -74, -148 \)

---

Final Answers:

1. \( \boxed{92, 94, 188} \)
2. \( \boxed{75, 71, -213} \)
3. \( \boxed{13, 21, 34} \)
4. \( \boxed{480, 484, 1452} \)
5. \( \boxed{6, 1, 4} \)
6. \( \boxed{31, 28, 34} \)
7. \( \boxed{480, 484, 1452} \)
8. \( \boxed{-8.5, -17, -8.5} \)
9. \( \boxed{25, 18, 24} \)
10. \( \boxed{-68, -74, -148} \)