1. SEQUENCES

2. Learning Objectives Generate terms of a simple sequence, given a rule, finding a term from the previous term Generate terms of a simple sequence, given a rule, finding a term given its position in the sequence To find the nth term of a linear sequence

3. Look at this sequence What is the second term of the sequence? 1 2 3 4 5 Term 4 7 10 13 16 Sequence What is the fourth term of the sequence? 7 13

4. Look at this sequence What do you notice about the numbers in the sequence? 1 2 3 4 5 Term Sequence What is the sixth term? Add 3 19 What is the seventh term? 3333 22 4 7 10 13 16 6 19 3 7 3 22

5. Look at this sequence What is the second term of the sequence? 1 2 3 4 5 Term 3 7 11 15 19 Sequence What is the fourth term of the sequence? 7 15

6. Look at this sequence What do you notice about the numbers in the sequence? 1 2 3 4 5 Term Sequence What is the sixth term? Add 4 23 What is the seventh term? 4444 27 3 7 11 15 19 6 23 4 7 4 27

7. This method of finding the next term in the sequence by adding the difference is known as the term to term method To get the next number in the sequence you simply add the difference! 1 2 3 4 5 Term Sequence 3 7 11 15 19 6 23 4 7 4 27

8. We need a method of finding any term in the sequence by using a rule to work out any number by using it’s position in the sequence. This method is known as the position to term method. 1 2 3 4 5 3 7 11 15 19 If we want to know the 10 th number we use a rule. 10 39

9. Look at this sequence The pattern is add 3 each time, but what is the rule? 1 2 3 4 5 Term Sequence 3333 4 7 10 13 16 The multiplier in the rule is always the same as the number you add for the term to term rule.

10. Look at this sequence 2 x 3 is not 7 4 x 3 is not 13 1 2 3 4 5 Term Sequence 4 7 10 13 16 The multiplier in the rule is always the same as the pattern number. When we multiply the term number by 3 we do not get the answer

11. This same sequence So the zero term is + 1 1 2 3 4 5 Term Sequence 3333 4 7 10 13 16 To find the rule we look at the zero term, the term BEFORE the sequence starts. 0 1 3 So the rule is: times by 3 then + 1 or 3n + 1

12. 1 2 3 4 5 Term Sequence 3333 4 7 10 13 16 0 1 3 So the rule is: times by 3 then + 1 The rule is: x 3 + 1 or 3n + 1 Finding the nth term

13. 1 2 3 4 5 Term Sequence 4 7 10 13 16 0 1 3 x 3 + 1 3n + 1 So the 10 th term is: 3 x 10 + 1 = 31 3 x 10 + 1 = 31 Finding the 10 th term :

14. 1 2 3 4 5 Term Sequence 4444 3 7 11 15 19 0 4 So the rule is: times by 4 then - 1 The rule is x 4 - 1 or 4n - 1 When the zero term is negative

15. 1 2 3 4 5 Term Sequence 3 7 11 15 19 0 4 x 4 - 1 So the 10 th term is: 4 x 10 - 1 = 39 4 x 10 - 1 = 39 Finding the 10 th term :

16. The End Now it’s your turn…