Worked examples


Look at the flow diagram below: input – 20


× 3 output


1 Write the rule for the nth term in the form. 2 Find the output number if the input number is 99. 3 Find the input number if the output number if 99.


Solutions 1 Tn = 3(n − 20)


2 T99 = 3(99 − 20) = 237


3 3(n − 20) = 99 ∴ n − 20 = 33 ∴ n = 53


Tn = (n – 20) × 3


Calculate the value of 3(n – 20) for n = 99 Solve for n if 3(n – 20) = 99


In order to work with number patterns and relationships, we need to be able to work with all these forms of representation, and be able to determine the missing input and output values.


Remember that to find input values we substitute in to the rule and then we simplify. To find output values, we substitute in to the rule and solve.


Exercise 1


1 The nth term of a pattern (Tn ) is given by the formula: Tn = 3n − 13 1.1 Find the value of the following terms:


1.1.1 the 6th term 1.1.2 the 13th term


1.2 Find the number of the term that is equal to: 1.2.1 −1


1.2.2 77


2 Look at the flow diagram below: input ÷ 5


+ 2 output


2.1 Write the rule for the nth term in the form. 2.2 Find the output number for each of these input numbers: 2.2.1 5


2.2.2 13 2.3.2 6,6


2.3 Find the input number for each of these output numbers: 2.3.1 4


2.2.3 31 2.3.3 11,4 1.1.3 the 29th term 1.2.3 131


Unit 3: Input and output values


129


CHAPTER 4


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