Math Worksheet Collection: Number Patterns | Media4Math - Free Printable

Let's solve each number sequence and find the rule for each one. We'll analyze the pattern step by step.

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1. Sequence: 6, 9, 12, 15, 18, 21

Step-by-step analysis:
- 9 - 6 = 3
- 12 - 9 = 3
- 15 - 12 = 3
- 18 - 15 = 3
- 21 - 18 = 3

✔ The numbers increase by 3 each time.

Rule: Add 3 to the previous term.
Or in formula form:
aₙ = 6 + (n - 1) × 3, where n is the position in the sequence.

👉 Answer: *Add 3 each time.*

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2. Sequence: 3, 9, 27, 81, 243, 729

Step-by-step analysis:
- 9 ÷ 3 = 3
- 27 ÷ 9 = 3
- 81 ÷ 27 = 3
- 243 ÷ 81 = 3
- 729 ÷ 243 = 3

✔ Each term is multiplied by 3.

This is a geometric sequence with common ratio 3.

Note:
- 3¹ = 3
- 3² = 9
- 3³ = 27
- 3⁴ = 81
- etc.

So the nth term is 3ⁿ.

👉 Answer: *Multiply by 3 each time.*

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3. Sequence: 42, 40, 38, 36, 34, 32

Step-by-step analysis:
- 40 - 42 = -2
- 38 - 40 = -2
- 36 - 38 = -2
- 34 - 36 = -2
- 32 - 34 = -2

✔ Decreases by 2 each time.

Rule: Subtract 2 from the previous term.

👉 Answer: *Subtract 2 each time.*

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4. Sequence: 14, 20, 26, 32, 38, 44

Step-by-step analysis:
- 20 - 14 = 6
- 26 - 20 = 6
- 32 - 26 = 6
- 38 - 32 = 6
- 44 - 38 = 6

✔ Increases by 6 each time.

Rule: Add 6 to the previous term.

👉 Answer: *Add 6 each time.*

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5. Sequence: 2, 6, 18, 54, 162, 486

Step-by-step analysis:
- 6 ÷ 2 = 3
- 18 ÷ 6 = 3
- 54 ÷ 18 = 3
- 162 ÷ 54 = 3
- 486 ÷ 162 = 3

✔ Each term is multiplied by 3.

Geometric sequence with ratio 3.

First term = 2 → 2 × 3^(n-1)

👉 Answer: *Multiply by 3 each time.*

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6. Sequence: 47, 42, 37, 32, 27, 22

Step-by-step analysis:
- 42 - 47 = -5
- 37 - 42 = -5
- 32 - 37 = -5
- 27 - 32 = -5
- 22 - 27 = -5

✔ Decreases by 5 each time.

Rule: Subtract 5 from the previous term.

👉 Answer: *Subtract 5 each time.*

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✔ Final Answers:

1. Add 3 each time.
2. Multiply by 3 each time.
3. Subtract 2 each time.
4. Add 6 each time.
5. Multiply by 3 each time.
6. Subtract 5 each time.

These are all arithmetic or geometric sequences with consistent rules. Let me know if you'd like them written in formula form!