Mathematics - Term 2 - Week 7

Patterns are sequences that follow a specific rule. For example, the sequence 2, 4, 6, 8 follows the rule of adding 2 each time. In algebra, we can express patterns using variables. For instance, if we let n represent the position in the sequence, we can write the nth term as 2n. This helps us generalize patterns and make predictions about future terms.

Consider the pattern 5, 10, 15, 20. The rule here is to add 5 each time. We can express this as a function: T(n) = 5n, where T(n) is the nth term. To find the 6th term, we substitute n with 6: T(6) = 5 * 6 = 30. Thus, the 6th term is 30.

Let's work together on the pattern 3, 6, 9, 12. What is the rule? (Students should identify that we are adding 3 each time.) Now, express this pattern using a formula. (The formula is T(n) = 3n.) Can anyone tell me what the 8th term would be? (Students should calculate T(8) = 3 * 8 = 24.)

Now it's your turn! Solve the following problems on your own: 1) Identify the next two terms in the pattern 7, 14, 21. 2) Write a formula for the pattern and find the 10th term. Remember to show your working clearly. After completing the problems, review your answers with a partner and discuss any mistakes.

• 8
• 9
• 10
• 11

Answer: 9

The pattern adds 2 each time, so 7 + 2 = 9.

• 4n
• 4n + 1
• 4n - 1
• 4n + 4

Answer: 4n

The pattern adds 4 each time, so the nth term is 4n.

Answer: 14

The pattern adds 3 each time, so the 5th term is 11 + 3 = 14.

• 7
• 8
• 9
• 10

Answer: 9

Substituting n with 4 gives T(4) = 2(4) + 1 = 9.

Answer: 10n

The pattern adds 10 each time, so the formula is 10n.

• 18
• 24
• 30
• 36

Answer: 18

The pattern adds 6 each time, so the 3rd term is 12 + 6 = 18.

• 2, 4, 6
• 1, 1, 1
• 3, 6, 9
• 5, 10, 15, 20, 22

Answer: 5, 10, 15, 20, 22

The last sequence does not follow a consistent rule as it jumps from 20 to 22.

Answer: 22

The pattern adds 3 each time, so the 7th term is 10 + 3 + 3 + 3 + 3 + 3 + 3 = 22.