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SEQUENCES

SEQUENCES. 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. Look at this sequence.

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SEQUENCES

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

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

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

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

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

  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 10 3 7 11 15 19 39 If we want to know the 10th number we use a rule.

  9. Look at this sequence Term 1 2 3 4 5 4 7 10 13 16 Sequence 3 3 3 3 The pattern is add 3 each time, but what is the rule? 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 Term 1 2 3 4 5 4 7 10 13 16 Sequence 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 2 x 3 is not7 4 x 3 is not13

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

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

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

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

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

  16. The End Now it’s your turn…

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