Mathematics - Term 3 - Week 5

Patterns are sequences that follow a specific rule or formula. In mathematics, we often encounter numerical patterns, such as arithmetic and geometric sequences. An arithmetic sequence adds a constant value to each term, while a geometric sequence multiplies each term by a constant factor. Recognizing these patterns helps us predict future terms and understand relationships between numbers.

Algebra involves using symbols and letters to represent numbers in equations and expressions. This allows us to formulate general rules and solve problems systematically. For example, in the expression 2x + 3 = 11, 'x' is a variable that can take different values. Solving for 'x' helps us find the unknown quantity.

Consider the sequence: 2, 5, 8, 11, ... This is an arithmetic sequence where each term increases by 3. To find the 10th term, we can use the formula for the nth term: a_n = a_1 + (n - 1)d, where a_1 is the first term and d is the common difference. Here, a_1 = 2, d = 3, and n = 10. Thus, a_10 = 2 + (10 - 1) * 3 = 2 + 27 = 29.

Let's solve the equation 3x - 4 = 11. First, we add 4 to both sides to isolate the term with 'x': 3x = 15. Next, we divide both sides by 3 to solve for 'x': x = 5. This means that when x is 5, the equation holds true.

Now, let's identify the pattern in the following sequence: 1, 4, 9, 16, ... What do you notice? Each term is a perfect square: 1^2, 2^2, 3^2, 4^2. Can you find the next two terms? The next terms would be 25 (5^2) and 36 (6^2).

Let's solve the equation 5x + 2 = 17 together. First, subtract 2 from both sides: 5x = 15. Now, divide by 5: x = 3. Can anyone explain why we performed these steps? It's important to isolate the variable to find its value.

Now it's your turn! Solve the following problems on your own: 1) Find the 5th term of the sequence 3, 6, 9, ... 2) Solve the equation 4x - 7 = 9. Show your working clearly and be prepared to discuss your solutions with a partner.

After completing the problems, review your answers with a partner. Discuss any mistakes you made and how you can correct them. Understanding where you went wrong is crucial for improving your problem-solving skills.

• 10
• 12
• 14
• 16

Answer: 10

The sequence increases by 2 each time, so the next term is 8 + 2 = 10.

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

Answer: 1, 3, 5, 7

This sequence increases by a constant difference of 2.

Answer: x = 4

Subtract 3 from both sides to get 2x = 8, then divide by 2.

• 30
• 35
• 40
• 45

Answer: 35

This is an arithmetic sequence with a common difference of 5. The 7th term is 5 + (7-1) * 5 = 35.

Answer: x = 3

Add 9 to both sides to get 3x = 9, then divide by 3.

• x + 5
• 5 + x
• 5x
• x - 5

Answer: x + 5

Both x + 5 and 5 + x are correct, but x + 5 is the standard form.

Answer: 19

This is an arithmetic sequence with a common difference of 2. The 10th term is 1 + (10-1) * 2 = 19.

• x = 2
• x = 4
• x = 6
• x = 8

Answer: x = 6

First, divide both sides by 4 to get x - 2 = 2, then add 2.