Worked examples


The patterns in the previous example are defined by the general rules below. Use each rule to calculate the value of the 10th term in the pattern.


1 Tn = 2n − 1


Solutions 1 T10 = 2(10) − 1 = 19 2 T10 = 1


_____ 10 + 2 = 1


___ 12


3 T10 = 102 − 1 = 99 Exercise 2


1 Use the rule: “any term in this pattern is one-third of the previous term” and write down the first four terms of each pattern below, if: 1.1 the 3rd term is 27


1.2 the 2nd term is 6


1.3 the 5th term is 1 2 For each of the number patterns below, work out the rule for the nth term. Use your rule to calculate the 10th term of the pattern.


2.1 2; 5; 10; 17; … 2.3 99; 97; 95; 93; …


2.5 −100; −97; −94; −91; … 2.4


2.2 −200; −150; −100; −50; … 4 ; …


1; 1 __


2.6 a + b; 2a + b2; 3a + b3; 4a + b4; …


2 ; 1 __


3 ; 1 __


3 The numbers below have an interesting pattern in common. 89 = 81 + 92 135 = 11 + 32 + 53 598 = 51 + 92 + 83 2 427 = 21 + 42 + 23 + 74 2 646 798 = 21 + 62 + 43 + 64 + 75 + 96 + 87


3.1 Check the calculations for each number above. 3.2 Write down the rule for the pattern in these numbers in your own words.


3.3 Test each of the following numbers to see whether they also obey the rule above: 3.3.1 175


3.3.2 253


4 Look at the table below: Number


Square 101


11 112 = 121 10 201


1 001 1 002 001 Cube


113 = 1 331 1 030 301


1 003 003 001 3.3.3 518 Fourth power


114 = 14 641 104 060 401


1 004 006 004 001 3.3.4 1 306 2 Tn = 1


____ 2 + n , or 1


____ n + 2 3


Tn = n2 − 1


Calculate the value of 2n – 1 for n = 10. Calculate the value of 1


____ n + 2 for n = 10.


Calculate the value of n2 – 1 for n = 10.


126 Chapter 4: Patterns, functions and relationships


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