Mathematics - Term 1 - Week 9

Patterns are sequences that follow a specific rule or formula. In mathematics, recognizing patterns helps us predict future numbers in a sequence. For example, the sequence 2, 4, 6, 8 follows a pattern where each number increases by 2. We can express this pattern using algebraic expressions, such as n = 2k, where k is a whole number.

Consider the pattern 5, 10, 15, 20. The rule here is that each number increases by 5. We can express this as an algebraic expression: a_n = 5n, where n represents the position in the sequence (1, 2, 3, ...). To find the 5th term, we substitute n with 5: a_5 = 5 * 5 = 25.

Let's work together on the sequence 3, 6, 9, 12. What is the next term? Notice that each term increases by 3. Therefore, the next term is 12 + 3 = 15. Now, can anyone express this pattern using an algebraic expression? Yes, it can be expressed as a_n = 3n.

Now it's your turn! Solve the following problems: 1) Identify the next term in the sequence 1, 4, 7, 10. 2) Write an algebraic expression for the sequence 2, 5, 8, 11. Show your working clearly and be prepared to discuss your methods with the class.

• 10
• 12
• 14
• 16

Answer: 10

The pattern increases by 2, so the next term is 8 + 2 = 10.

• 3n
• n + 3
• 3n + 1
• n^2

Answer: 3n

The sequence increases by 3 for each term, which can be expressed as 3n.

Answer: 25

The pattern increases by 5, so 20 + 5 = 25.

• 2n
• 2n - 1
• n + 1
• n^2

Answer: 2n - 1

The sequence consists of odd numbers, which can be expressed as 2n - 1.

Answer: 32

The pattern increases by 8, so 24 + 8 = 32.

• 2, 4, 8, 16
• 1, 3, 5, 7
• 5, 10, 20, 40
• 3, 6, 12, 24

Answer: 1, 3, 5, 7

An arithmetic sequence has a constant difference, which is 2 in this case.

Answer: 4n

The sequence increases by 4, which can be expressed as 4n.

• 40
• 50
• 60
• 70

Answer: 40

The pattern increases by 10, so 30 + 10 = 40.