Grade 6 Patterns in Mathematics

 

🔹 What is a Pattern?

A pattern is a sequence of numbers that follows a rule.

👉 Example:

0, 1, 2, 3, 4, … (each time +1)

2, 4, 6, 8, … (each time +2)

🔹 What is Number Theory?

Number Theory is a branch of Mathematics that studies numbers and their patterns.

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🔹 What are Number Sequences?

A number sequence is an ordered list of numbers that follows a specific rule.

👉 Examples:

• 1, 2, 3, 4, … (Counting numbers)

• 2, 4, 6, 8, … (Even numbers)

• 1, 3, 5, 7, … (Odd numbers)

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✍️ How to write in exam:

Patterns in Numbers:
“A pattern is a sequence of numbers that follows a certain rule.”

Number Sequence:
“A number sequence is an ordered list of numbers that follows a specific rule.”

Figure it out:

1. Can you recognise the pattern in each of the sequences in Table 1?

Yes, each sequence follows a specific mathematical rule where each number depends on its position or the numbers before it.
2. Sequences with Next Three Numbers and Rules

Here is Table 1 exactly as it appears in your image:

Table 1: Examples of number sequences

Sequence	Name
1, 1, 1, 1, 1, 1, 1, ...	(All 1's)
1, 2, 3, 4, 5, 6, 7, ...	(Counting numbers)
1, 3, 5, 7, 9, 11, 13, ...	(Odd numbers)
2, 4, 6, 8, 10, 12, 14, ...	(Even numbers)
1, 3, 6, 10, 15, 21, 28, ...	(Triangular numbers)
1, 4, 9, 16, 25, 36, 49, ...	(Squares)
1, 8, 27, 64, 125, 216, ...	(Cubes)
1, 2, 3, 5, 8, 13, 21, ...	(Virahāṅka numbers)
1, 2, 4, 8, 16, 32, 64, ...	(Powers of 2)
1, 3, 9, 27, 81, 243, 729, ...	(Powers of 3)

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Table sequences and pattern with next 3 numbers

1. 1, 1, 1, 1, 1, …
   👉 Pattern: All numbers have 1
   ✅ Next: 1, 1, 1

2. 1, 2, 3, 4, 5, 6, 7, … (Counting numbers)
   👉 Pattern: Adding  +1
   ✅ Next: 8, 9, 10

3. 1, 3, 5, 7, 9, 11, … (Odd numbers)
   👉 Pattern: Add +2 (odd numbers)
   ✅ Next: 13, 15, 17

4. 2, 4, 6, 8, 10, 12, … (Even numbers)
   👉 Pattern: Add +2 (even numbers)
   ✅ Next: 14, 16, 18

5. 1, 3, 6, 10, 15, 21, 28, … (Triangular numbers)
   👉 Pattern: +2, +3, +4, +5, +6…
   ✅ Next:
   28 + 8 = 36
   36 + 9 = 45
   45 + 10 = 55

6. 1, 4, 9, 16, 25, 36, 49, … (Squares)
   👉 Pattern: \((n^2) =(1^2, 2^2, 3^2,\dots)\)
   ✅ Next: 64, 81, 100

7. 1, 8, 27, 64, 125, 216, … (Cubes)
   👉 Pattern: \((n^3) =(1^3, 2^3,\dots) \)
   ✅ Next: 343, 512, 729

8. 1, 2, 3, 5, 8, 13, 21, … (Virahanka / Fibonacci)
   👉 Pattern: Add last two numbers
   ✅ Next:
   13 + 21 = 34
   21 + 34 = 55
   34 + 55 = 89

9. 1, 2, 4, 8, 16, 32, 64, … (Powers of 2)
   👉 Pattern: Each time  ×2
   ✅ Next: 128, 256, 512

10. 1, 3, 9, 27, 81, 243, 729, … (Powers of 3)
    👉 Pattern: Each time  ×3
    ✅ Next: 2187, 6561, 19683

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