Mathematics - Term 3 - Week 5

Patterns are sequences that follow a specific rule. In mathematics, they can be numerical or algebraic. For example, the sequence 2, 4, 6, 8 is a numerical pattern where each number increases by 2. Algebraic patterns can involve variables, such as the expression 2n, where n represents a number. Recognizing these patterns helps in predicting future terms and understanding algebraic relationships.

Consider the pattern 3, 6, 9, 12. This is an arithmetic sequence where each term increases by 3. To find the next term, we add 3 to the last term: 12 + 3 = 15. Now, if we express this pattern algebraically, we can say the nth term is given by the formula 3n, where n is the position in the sequence (1, 2, 3, ...).

Let's work together on the pattern 5, 10, 15, 20. What is the rule? Students should recognize that each term increases by 5. Now, let's express this pattern algebraically. If we let n represent the term number, we can write the nth term as 5n. Can anyone tell me what the 6th term would be? (Answer: 30).

Now it's your turn! Solve the following problems on your own. 1) Identify the next two terms in the pattern 4, 8, 12, 16. 2) Write the algebraic expression for the pattern where each term increases by 7 starting from 1. Show your working clearly and be prepared to explain your reasoning.

• 8
• 9
• 10
• 11

Answer: 9

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

• n + 1
• 2n
• n^2
• n + 2

Answer: 2n

Each term is double the position number, hence 2n.

Answer: 40, 50

The pattern increases by 10 each time.

• Add 2
• Add 3
• Add 5
• Add 10

Answer: Add 5

Each term increases by 5.

Answer: 12

Substituting n = 4 gives 3 * 4 = 12.

• n + 1
• n^2
• 2n
• 3n

Answer: n^2

These numbers are perfect squares of the integers.

Answer: Correct, the next term is 10.

The pattern correctly continues by adding 2.

• 9
• 10
• 11
• 12

Answer: 11

Substituting n = 5 gives 2 * 5 + 1 = 11.