M1W1 Generating Patterns (sequence and patterns)

sequence and patterns

1. GENERATING PATTERNS MATHEMATICS 10 – MODULE 1 Prepared By: Chriza D. Suarez

2. OBJECTIVES M1: GENERATING PATTERNS

3. LET’S RECALL M1: GENERATING PATTERNS CAN YOU SPOT THE PATTERN? Identify what comes next in the pattern of figures or list of numbers. 60 1,280 7.5

4. Lesson 2 M1: GENERATING PATTERNS SEQUENCE PATTERN is also known as a SEQUENCE . is an arrangement of elements or numbers that usually follow a particular rule. It can be finite (elements can be counted) or infinite (the pattern goes on).

5. Lesson 1 M1: GENERATING PATTERNS FINITE SEQUENCE (can be counted) example: 0, 3, 6, 9, 12, 15 This sequence has exactly 6 elements INFINITE SEQUENCE (cannot be counted) example: 10, 20, 30, 40 … Three dots mean it keeps going and going.

6. Lesson 1 M1: GENERATING PATTERNS Can you give an example of a finite sequence?

7. Lesson 1 M1: GENERATING PATTERNS Can you give an example of an infinite sequence?

8. Lesson 1 M1: GENERATING PATTERNS SEQUENCE is a set of numbers written in a specific order: , … Each element in a sequence is called a TERM . It can be represented by using where n is the position of the term . Ex. 1 : 0, 3, 6, 9, 12, 15 The first term is 0, the second term is 3, the third term is 6, = 9 and = 12. Ex. 2: 0, 20, 30, 40 … = 10, = 20, = 30, = 40, etc.  

9. Lesson 1 M1: GENERATING PATTERNS SEQUENCE

10. Lesson 1 M1: GENERATING PATTERNS LET’S APPLY 29 35 41 Add 6 -56 -112 -224 Multiply to 2 * *

11. Lesson 2 M1: GENERATING PATTERNS FINDING THE NEXT TERM OF A SEQUENCE GIVEN ITS GENERAL TERM GENERAL TERM OR NTH TERM RULE is used to generate and continue the sequence. Example: Find the first 5 terms of the sequence given the general term: . Given: The general term: = n + 3   Solution: First term: = 1 + 3 = 4 Second term = 2 + 3 = 5 Third term = 3 + 3 = 6 Fourth Term = 4 + 3 = 7 Fifth Term = 5 + 3 = 8 The first five terms of the sequence are 4, 5, 6, 7, 8.  

12. Lesson 2 M1: GENERATING PATTERNS FINDING THE NEXT TERM OF A SEQUENCE GIVEN ITS GENERAL TERM Example: Ex. 4 Find the next three terms of where the first term is 5. Given: General term: First term:   Solution: Second term = 7(2) – 2 = 12 Third term = 7(3) – 2 = 19 Fourth Term = 7(4) – 2 = 26 The next three terms of the sequence are 12, 19 and 26 .  

13. Lesson 1 M1: GENERATING PATTERNS LET’S APPLY Sol #1 = 2+1   * * 3 Sol #4    

14. Lesson 3 M1: GENERATING PATTERNS FINDING THE GENERAL TERM OF A SEQUENCE

15. Lesson 3 M1: GENERATING PATTERNS FINDING THE GENERAL TERM OF A SEQUENCE Example: Find the general term of the sequence: 2, 4, 6, 8, …. Step 1: Write the given terms in a table. Condition 1: It fits the given. Answer: The general term of the sequence 2, 4, 6 8, ... is defined by the formula .   Step 2: Study the pattern rule. Step 3: Check if the expression/formula, fits the given value by substitution. Checking: If =2n , = 2(1) =2; = 2(3) =6 = 2(2) =4 = 2(4) =8   Since we repeat adding 2 to each value of the term, the short way to write this is by using multiplication expression. That is .  

16. Lesson 3 M1: GENERATING PATTERNS FINDING THE GENERAL TERM OF A SEQUENCE Example: What is the 100 th term of the sequence 8, 13, 18, 23, . . . ? Step 1: Write the given terms in a table. Condition: Step 2: Study the pattern rule. Step 3: Check if the expression/formula, fits the given value by substitution.

17. Seatwork #2 Complete the table below by substituting the given values of to and list down the terms of the sequence.   1 2 3 4 SEQUENCE -2 1 4     3 6       -5         1                 1 2 3 4 SEQUENCE -2 1 4     3 6       -5         1                

18. Lesson 2 SEQUENCE FINDING THE NEXT TERM OF A SEQUENCE GIVEN ITS GENERAL TERM - is a function, where the domain is a set of consecutive positive integers beginning with 1 GENERAL TERM OR NTH RULE - is used t generate and continue the sequence

19. Some of the function values, also known as TERMS of the sequence are as follows: , , , The first term of the sequence is denoted as , the fifth term as , and the nth term, or general term as .