📊 Part 1: Identifying Linear Patterns

1. Look at this pattern table. What is the constant increase?

Pattern A:

Term (n): 1, 2, 3, 4, 5

Value (T): 4, 7, 10, 13, 16

Increases by 2

Increases by 3

Increases by 4

Increases by 5

2. Complete this pattern table:

Pattern B: Starting at 20, decreasing by 4 each time

Term (n): 1, 2, 3, 4, 5

Value (T): 20, _____, _____, _____, _____

3. Which of these sequences shows a linear pattern?

2, 4, 8, 16, 32

5, 9, 13, 17, 21

1, 4, 9, 16, 25

3, 6, 12, 15, 30

🔢 Part 2: Algebraic Equations and Rules

4. For Pattern A from Question 1 (4, 7, 10, 13, 16...), write the algebraic rule:

T = _____________

5. A linear pattern follows the rule T = 5n + 2. Complete the table:

Term (n): 1, 2, 3, 4, 6

Value (T): _____, _____, _____, _____, _____

6. Match each pattern rule to its description:

T = 3n

T = 2n + 5

T = 15 - 2n

Starts at 7, increases by 2

Starts at 13, decreases by 2

Starts at 3, increases by 3

📈 Part 3: Making Predictions and Graphing

7. Using the rule T = 4n + 1, predict the value for:

a) Term 10: T = _____

b) Term 20: T = _____

c) Term 50: T = _____

8. A swimming pool is being filled. After 1 hour there are 500 litres, after 2 hours there are 800 litres, after 3 hours there are 1100 litres.

a) What is the constant increase per hour? _____ litres

b) Write the rule: T = _____________

c) How many litres will be in the pool after 6 hours? _____ litres

9. On the grid below, plot the points for the pattern T = 2n + 3 where n = 1, 2, 3, 4, 5:

10. Explain in your own words: How can you tell if a pattern is linear just by looking at a table of values?

Linear Patterns Exploration

Linear Patterns Exploration

📊 Part 1: Identifying Linear Patterns

🔢 Part 2: Algebraic Equations and Rules

📈 Part 3: Making Predictions and Graphing

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