Mathematics - Term 2 - Week 7

Patterns are sequences that follow a specific rule. For example, in the sequence 2, 4, 6, 8, the pattern is that each number increases by 2. Identifying patterns helps us predict future numbers in the sequence. In algebra, we often use variables to represent unknown values, allowing us to express patterns in a more general form. For instance, the pattern above can be expressed as 2n, where n is a positive integer.

Consider the pattern: 5, 10, 15, 20. Here, each term increases by 5. We can express this pattern using the formula: a_n = 5n, where n is the term number. For example, to find the 4th term (n=4), we calculate a_4 = 5 * 4 = 20. This method can be applied to various patterns to find any term in the sequence.

Let's work on identifying the pattern in the following sequence: 3, 6, 9, 12. What is the rule? Students should notice that each number increases by 3. Now, let's express this pattern algebraically. The nth term can be represented as a_n = 3n. Can anyone tell me what the 5th term would be? (Students should calculate a_5 = 3 * 5 = 15).

Now it's your turn! Solve the following problems independently. 1) Find the 7th term of the sequence defined by a_n = 4n. 2) If the pattern is 1, 4, 9, 16, what is the 6th term? Write down your working clearly to show how you arrived at your answers.

• 2
• 4
• 6
• 8

Answer: 6

To find the 3rd term, substitute n=3 into the formula: a_3 = 2 * 3 = 6.

• 1, 2, 3, 4
• 2, 6, 10, 14
• 5, 9, 13, 17
• 3, 7, 11, 15

Answer: 5, 9, 13, 17

In the sequence 5, 9, 13, 17, each term increases by 4.

Answer: a_n = 10n

The pattern increases by 10, so the nth term can be expressed as 10n.

• 14
• 15
• 16
• 17

Answer: 16

Substituting n=5 gives a_5 = 3 * 5 + 1 = 16.

Answer: 8

The sequence is 1, 2, 4, 8, so the 4th term is 8.

• a_n = 6n
• a_n = 7n
• a_n = 7n + 1
• a_n = 7n - 1

Answer: a_n = 7n

Each term is a multiple of 7, so the correct expression is a_n = 7n.

Answer: 64

The 8th term is a_8 = 8^2 = 64.

• 2
• 3
• 4
• 5

Answer: 3

The difference between consecutive terms is 3.