Worked examples
Write down the next three terms in each of the following patterns: 1 −32; 16; −8; 4; … 3 7; 10; 15; 22; …
2 4
Solutions 1
___ −2 = −2
4
___ −2 = 1
___ −2 = − 1
−2 1
__ 2
The next three terms are −2; 1; − 1
2 Numerator = 1; 2; 3; 4; … Next terms = 5; 6; 7
Denominator = 2; 9; 16; 23… Next terms = 30; 37; 44
The next three terms are 5
___ 30 ; 6
___ 37 ; 7
___ 44
3 22 + 9 = 31 31 + 11 = 42 42 + 13 = 55 The next three terms are 31; 42; 55
__ 2
__ 2 ; 2
1 x; 3x; 5x; 7x; …
__ 9 ; 3
___ 16 ; 4
___ 23 ; …
First find the rule that connects the terms in the pattern. Each term is half the previous one and has the opposite sign. The rule is therefore T ÷ –2 Now work out each of the new terms by applying the rule.
Treat the numerators and the denominators separately. The rule for the numerator is T + 1 The rule for denominator is T + 7
Now combine the next three numerators and denominators to find the three terms.
To get the next term, add 3, then add 5, then add 7. In other words, add two more each time. Write out the next three terms.
4 The next three terms are 9x; 11x; 13x To get to the next term, add 2x each time.
Exercise 2
1.1 Copy and complete the table below: 12
22 32 42 52
72 82
102
= = = = = = = = = =
1 4
16 36 81 = 1 = 1 + 3
= 1 + 3 + 5 =
= 1 + 3 + 5 + 7 + 9
= 1 + 3 + 5 + 7 + 9 + 11 =
= 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 =
= 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 1.2 Describe the number pattern above in words. Unit 1: Investigate and extend patterns 121
CHAPTER 4
Page 1 |
Page 2 |
Page 3 |
Page 4 |
Page 5 |
Page 6 |
Page 7 |
Page 8 |
Page 9 |
Page 10 |
Page 11 |
Page 12 |
Page 13 |
Page 14 |
Page 15 |
Page 16 |
Page 17 |
Page 18 |
Page 19 |
Page 20 |
Page 21 |
Page 22 |
Page 23 |
Page 24 |
Page 25 |
Page 26 |
Page 27 |
Page 28 |
Page 29 |
Page 30 |
Page 31 |
Page 32 |
Page 33 |
Page 34 |
Page 35 |
Page 36 |
Page 37 |
Page 38 |
Page 39 |
Page 40 |
Page 41 |
Page 42 |
Page 43
