Mr Froggett’s Sequence Fun Fair.

# Mr Froggett’s Sequence Fun Fair.

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## Mr Froggett’s Sequence Fun Fair.

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1. Mr Froggett’s Sequence Fun Fair.

2. Role up, role up! Who feels lucky today? • 3 shots for a pound. • Every hit gets a prize • Anyone want a go?

3. Mr Froggett’s Fun Fair

4. Mr Froggett’s Fun Fair

5. Mr Froggett’s Fun Fair

6. Mr Froggett’s Fun Fair

7. Mr Froggett’s Fun Fair

8. Mr Froggett’s Fun Fair

9. 1 1 3 2 5 3 7 4 9 5 Mr Froggett’s Fun Fair Row

10. Mr Froggett’s Fun Fair Row 1 1 3 2 +2 +2 +2 +2 5 3 7 4 9 5

11. Mr Froggett’s Fun Fair 2 1 3 4 5 9 1 3 5 7 +2 +2 +2 +2 +2 Nth term = __ x term + or - ___ n

12. Term(n) x 2 9 1 3 5 7 Mr Froggett’s Fun Fair 2 1 3 4 5 2 4 6 8 10 2 x n Nth term = +2 x n + or - ___

13. Term(n) 9 1 3 5 7 2n - Mr Froggett’s Fun Fair 2 1 3 4 5 2 4 6 8 10 2n -1 -1 -1 -1 -1 -1 Difference 2 x n Nth term = +2 x n + or -

14. 17 1 1 9 Mr Froggett’s Fun Fair 2n – 1 = Nth term = 2 x n - 1

15. Your turn • Find the nth term, the next two numbers in the sequence and the 10th term. • 1, 5, 9, 13, 4n – 3 37 • 17, 15, 13, 11, -2n + 19 -1 • 7, 10, 13, 16 3n + 4 34 • 2, 11, 20, 29 9n – 7 83 • 21, 14, 7, 0 -7n + 28 -42

16. 1 1 4 2 9 3 16 4 16 25 25 5 Mr Froggett’s Quadratic Fun Fair Row

17. Mr Froggett’s Fun Fair Row 1 1 4 2 +3 +5 +7 +9 +2 +2 +2 +2 9 3 Therefore if the second difference is +2 the rule must have x2 in it. 16 4 25 5

18. Term(n) n2 25 1 4 9 16 Mr Froggett’s Fun Fair 2 1 3 4 5 1 4 9 16 25 n2 Nth term = n2 + or - ___

19. Term(n) 25 1 4 9 16 Mr Froggett’s Fun Fair 2 1 3 4 5 1 4 9 16 25 n2 0 0 0 0 0 0 0 Difference Nth term = n2 + or - ___ Nth term = n2

20. Mr Froggett’s Fun Fair 2 1 3 4 5 2 8 18 32 50 +6 +10 +14 +18 +4 +4 +4 What effect would it have on the rule if the second difference became + 4?

21. Mr Froggett’s Fun Fair

22. Nth term = 2n2 + 4n – 3

23. Your turn • Find the nth term and the 10th term. • 10, 18, 28, 40 • 4, 9, 17, 28 • 7, 15, 25, 37 • 2, 5, 10, 17, 26