1.1.5 Number patterns

NUMBER PATTERNS

Learning Outcomes

Recognize and continue arithmetic and geometric patterns.

Describe rules governing number patterns.

Lesson Notes

Arithmetic Sequence:

Each term increases or decreases by a constant value.

Example: 2, 4, 6, 8, 10, …

Rule: Add 2 each time.

Geometric Sequence:

Each term is multiplied by a constant number.

Example: 3, 6, 12, 24, …

Rule: Multiply by 2.

Worked Example

Find the 6th term of 3, 6, 9, 12, …

Common difference = 3

aₙ = a₁ + (n − 1)d

a₆ = 3 + (6 − 1) × 3 = 3 + 15 = 18

Exercise 5

1. Write the next three terms: 4, 8, 12, 16, …

2. Find the 10th term of 5, 10, 15, 20, …

3. Continue the pattern: 2, 6, 18, 54, …