1. Numeric and geometric patterns
Chapter 4, Page 55

2. 1.Patterns with a constant difference
E.g 1: 3; 6; 9; …; …; …
E.g 2: -4; -6; -8; …; …; …
E.g 3: ; ; ; …; …; …
To find the general formula:
Find the constant difference
Multiply this by “n”
Substitute 1 in the place of “n”
What must I add or subtract to get the first term?
CHECK!

3. 2.Patterns without a constant difference
E.g 1: 2; 3; 5; 8; …; …; … E.g 2: 5; 2; -4; -13; …; …; …

4. 3.Patterns with an exponential difference
E.g 1: 1; 4; 9; 16; …; …; … E.g 2: 2; 4; 8; 16; …; …; …

5. 4.Using a table E.g 1: Study the sequence made with matches
Pattern number 1 2 3 4 n
100
Number of boxes
Number of matches used

6. Complete the tables Input value 1 2 3 4 5 13 29 n Output value - 2 - 4
- 6
- 8
Input value 1 2 3 4 5 10 25
Output value
- 1
- 4 8

7. Consider the pattern:
Figure 1 2 3 4
100 n
Number of matchsticks

8. Consider the pattern: Determine a rule:
Which arrangement has 225 balls?

9. Consider the pattern: Ex 4.1 Page 55 #1b,d,f,h 2a,b 4 5a,b
Draw pattern 5 and state how many dots it has.
Determine a rule.
How many dots in triangle 100?
Ex 4.1 Page 55 #1b,d,f,h 2a,b 4 5a,b
Ex 4.2 Page 58 # 1RHS, 2a,b,g

10. Exercise 4.1: Answers
1b) 29; 34; 39 d) -17; -20; -23 f) 6 7 ; 7 8 ; 8 9 h) 37; 50; 65 2a)
INPUT 5 6 7 8 9 10
OUTPUT 11 14 17 20 23

11. Exercise 4.1: Answers
2b) 4a) b) 4; 7; 10 c) 13; 16; 19 d) 28 e) Picture number x 3; and then add 1
INPUT 6 7 8 9 10
OUTPUT
243
-729
2187
-6561
19683

12. Exercise 4.1: Answers
5a) b) Pattern number x 4; then add 1 c) CANNOT DO YET
Pattern 1 2 3 4 5 6 7 8
# of squares 9 13 17 21 25 29 33

13. Exercise 4.2: Answers
1b) 8; 1; -6 d) -3; 1; 5 f) 20; 27; 35 h) -10.5; -13; j) 32; -64; 128 l) 1; 1 3 ; 1 9 n) ; ; p) 11 3 ; 13 3 ; 15 3

14. Exercise 4.2: Answers
2a) 4; 12; 20 b) 28 Toothpicks g) Tn = 8n - 4