Writing the rule in words
We are first going to look at some examples of writing the general rule for a pattern in words.
Worked examples
For each of the following patterns, find the general rule. Write this rule in words. 1 1; 3; 5; 7; …
2 Solutions
1 Add 2 to each term to get the next term.
2 Multiply each term by 2 to get the next term.
3 Divide each term by −2 or multiply each term by − 1
or multiply each term by −0,5 to get the next term.
__ 2
Exercise 1
1 The general terms of some patterns are given below. For each pattern, calculate the first three terms as well as the 15th term.
1.1 Tn = 5n + 3 1.3 Tn = n2 − 1 2 n
1.5 Tn = 1 __
1.7 Tn = 3n − 1 + 1
1.2 Tn = 1,5n − 0,5 1.4 Tn = 3n2 − n 2n
1.6 Tn = 1 __
1.8 Tn = (−1)n.4n
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 your own words.
2.1 1; 0,1; 0,01; … 2.3 49; 7; 1; … 2.5 100; 10; √
2.2 3; 8; 13; …
___ 10 ; …
Writing the rule in algebra
As you saw in the last example above, there can be different ways of describing a pattern in words. It is often shorter and less confusing to write the general rule for a pattern in algebraic language. We are now going to look at some examples of this.
124 Chapter 4: Patterns, functions and relationships
2.4 256; 64; 16; … 2.6 1; 2; 6; 24; …
The numbers in the pattern all differ by 2. 6; 12; 24; 48; … 3 4; −2; 1; −0,5; …
Each number in the pattern is twice the previous number.
Each number in the pattern is half of the previous number, with the opposite sign to the previous number.
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