1. Number Patterns

2. Number patterns Key words: Pattern Sequence Rule Term Formula

3. 5 12 19 26 33 What is the next number? 30 What next? 37 What is the rule? Add 7

4. 8 11 14 17 20 What is the next number? 23 What next? 26 What is the rule? Add 3

5. 8 11 14 17 20 How can we find the 20 th term, or the 100 th term, without having to keep on adding 3s?

6. 8 11 14 17 20 We need to find a formula for the nth term.

7. 8 11 14 17 20 Start by drawing a table:

8. The formula has 2 parts: (i) difference x term number in this case:3n Term Number (n) 12345 nth term811141720

9. The formula has 2 parts: (i) difference x term number in this case:3n (ii) plus term “0” (the term before the first one!) in this case:5 Term Number (n) 012345 nth term811141720

10. 8 11 14 17 20 So for this pattern, nth term = 3n + 5 20 th term = 3x20 + 5 = 65 100 th term = 3x100 +5 = 305

11. For each pattern, find a) the rule to get from one term to the next b) the next 3 terms c) the nth term formula d) the 20 th term. 1. 7 9 11 13 2. 5 8 11 14 3. 6 10 14 18 4. 20 30 40 50 5. 18 36 54 72 Nth term: 20 th term: 2n + 545 3n + 262 4n + 282 10n + 10210 18n360

12. JRElse 2004