CHAPTER 4


1.2 −5; 5; −6; 6; −7; … 1.3 −2,5; −2; −1,5; −1; … 1.4 0; 1; 8; 27; …


__ 2 ; 1; 2; 4; …


1.5 6; 6,9; 6,96; 6,969; … 1.6 61; 60; 58; 55; … 1.7 x; 5x2; 125x3; …


1.8 a + 10b; a2 + 7b; a3 + 4b; …


2.1 5; 1; −3; −7; … 2.2 625; 125; 25; 5; … 2.3 1


3 The general terms of some patterns are given below. For each pattern, calculate the first three terms as well as the 15th term.


__ 9 ; 2


__ 3 ; …


3.1 Tn = n + 6


3.4 Tn = n2 + 2n 3.5 Tn = 4.3n 3.6 Tn = 4.3n


3.3 Tn = 5n ___


3.2 Tn = 2,5 − 1,5n 2


(2) (2) (2) (2) (2) (3)


4 You have a box that contains 50 matches. 4.1 Design your own geometric pattern using these matches. Show the first four stages of your pattern. You should not use more than the 50 matches that you have in total.


4.2 Copy and complete the table below: 1


Stage Number of matches


4.3 Work out the rule for the number of matches that you would need to make the nth stage of your pattern.


(2)


4.4 Use your rule from Question 4.3 to calculate the number of matches that you would need to make the 100th stage of your pattern.


(1) 2 3 4


__ 7 ; 4


__ 5 ; 8


Consolidation


1. Write down the next three terms in each of the following patterns: 1.1 1


(1) (1) (1) (1) (1) (2) (2) (2)


2 In each of the patterns below, you can work out any term by applying a rule to the previous term. Describe the rule for each pattern in words.


(1) (1) (2)


(2) (2)


138 Chapter 4: Patterns, functions and relationships


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